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603 reviewed resources for graphing exponential function

EngageNY

EngageNY Algebra I Module 3: Linear and Exponential Functions

For Teachers 9th - 12th Standards
The Algebra 1, Module 3 collection focuses on linear and exponential functions. The module's 26 lessons are divided into four topics: Linear and Exponential Sequences, Functions and Their Graphs, Transformations of Functions, and Using...
11 Items in Collection
Lesson Planet

Exponential Functions

For Teachers 8th - 11th Standards
Once your class masters the rules of exponents, it's time for graphing. Use a collection of resources, videos, and worksheets that start with guided help simplifying expressions and finishing with full graphing problems. 
EngageNY

EngageNY Algebra I Module 1: Relationships Between Quantities and Reasoning with Equations and Their Graphs

For Teachers 9th - 12th Standards
The Algebra 1, Module 1 collection is designed to help students develop fluency in writing, interpreting, and solving linear equations The 30 lessons are divided into four topics: An Introduction to Functions , the Structure of...
EngageNY

EngageNY Algebra I Module 5: A Synthesis of Modeling with Equations and Functions

For Teachers 9th - 12th Standards
The 10 lessons in the Algebra 1 Module 5 collection require students to synthesize what they have learned about functions. The module focuses on two topics: Elements of Modeling and Completing the Modeling Cycle. Assessments, exit...
3 Items in Collection
Lesson Planet

"Grade 9-12, Claim 2 & 4: Problem Solving & Communication Reasoning Supports"

For Teachers 9th - 12th Standards
Small but mighty, a collection of three resources features presentation slides that prepare high schoolers for the Smarter Balanced assessment. Claim 2 features problem solving questions drawn from all content areas. Claim 3 focuses on...
5 Items in Collection
Lesson Planet

Summer Math Projects

For Teachers 6th - 11th
Summer learning loss can be one of the most tragic things to happen to a student's academic success, as well as cause much frustration for educators. Stop the learning loss in math with five summer projects intended for middle and high...
35 Items in Collection
Lesson Planet

Common Core Math: 8th Grade

For Teachers 8th Standards
Check out the Common Core with a collection that represents all the 8th grade math standards. Most resources engage multiple standards but the main one is listed on the notes section of each tab. 
1 In 1 Collection
Lesson Planet

Graphing Exponential Functions

For Students 9th - 11th
Explore the concept of graphing exponential functions. High school mathematicians are given exponential functions such as y=2*3^x, and they graph them on a coordinate plane.  They are given two exponential graphs and must write an...
Lesson Planet

Graphing Exponential Functions

For Teachers 8th - 10th Standards
Once you know how to graph y = b^x, the sky's the limit. Young mathematicians learn to graph basic exponential functions and identify key features, and then graph functions of the form f(x) = ab^(x – h) + k from the function f(x) = b^x.
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Lesson Planet

Exponential Functions and Their Graphs

For Students 9th - 12th
Expand your knowledge on exponential growth! A concept video features the definition of an exponential function. Eight problem videos cover graphing exponential functions, identifying exponential growth and decay, and applying...
7:15
Lesson Planet

How Do You Graph an Exponential Function Using a Table?

For Teachers 8th - 11th
One way to get values to be able to graph an exponential function is to make a table. This seems pretty straightforward. Set up a table to plug in random values for x. Then put those values into the equation to get the y-values. These...
Lesson Planet

Exponential Functions

For Teachers 11th - 12th
With this two-page resource, learners evaluate and graph exponential functions. There are 48 questions using logs and exponents as the parent function.
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Exponential Functions

For Teachers 11th
Analyze functions by their shape and equation and identify decay and growth based on the equation given. Learners graph their exponential functions and differentiate it using the logarithmic versus the exponential function.
Lesson Planet

Explore Learning Exponential Functions

For Teachers 10th - 12th
High schoolers graph exponential equations and solve application problems using exponential functions. They re-enact a story about a peasant worker whose payment for services is rice grains doubled on a checker board. They place M &...
Lesson Planet

Exponential Functions

For Teachers 8th - 10th
Young scholars graph exponential equations of the form y=Ma. They understand the effects of M, a, and k on the graph. They solve application problems using exponential functions.
Lesson Planet

Matchstick Math: Using Manipulatives to Model Linear, Quadratic, and Exponential Functions

For Teachers 9th - 10th
Playing with matches (unlit, of course) becomes an engaging learning experience in this fun instructional unit. Teach pupils how to apply properties of exponential functions to solve problems. They differentiate between quadratic and...
Lesson Planet

Careers in Banking: Working with Exponential Growth

For Teachers 8th Standards
Emphasize the importance of investing and money management at a young age. Pupils create exponential equations to model how different investments grow. The class describes the two investments and look at the effects of the parameters of...
1 In 1 Collection
EngageNY

Graphs of Exponential Functions and Logarithmic Functions

For Teachers 10th - 12th Standards
Graphing by hand does have its advantages. The 19th installment of a 35-part module prompts pupils to use skills from previous lessons to graph exponential and logarithmic functions. They reflect each function type over a diagonal line...
1 In 1 Collection
EngageNY

Transformations of the Graphs of Logarithmic and Exponential Functions

For Teachers 10th - 12th Standards
Transform your lesson on transformations. Scholars investigate transformations, with particular emphasis on translations and dilations of the graphs of logarithmic and exponential functions. As part of this investigation, they examine...
Lesson Planet

Too Hot To Handle – Comparing Linear and Exponential Functions

For Teachers 9th - 12th Standards
What do forest fires have to do with math? Learners use their knowledge of linear and exponential functions to explore a real-world scenario involving a forest fire. The lesson employs group work and discussion to assist learners as they...
1 In 1 Collection
Lesson Planet

Introduction to Exponential Functions

For Teachers 8th - 10th Standards
This lesson plan begins with a review of linear functions and segues nicely over its fifteen examples and problems into a deep study of exponential functions. Linear and exponential growth are compared in an investment task. Data tables...
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Linear and Exponential Functions

For Teachers 8th - 11th Standards
This comprehensive unit on linear and exponential functions provides numerous clearly-written worksheets. Topics include graphing linear equations, solving systems of equations algebraically and by graphing, identifying the domain and...
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Domain and Range of Exponential Functions

For Teachers 7th - 9th
Students identify the domain and range of exponential functions. In this algebra lesson, students graph the exponential functions and differentiate between growth and decay. They use GeoGebra to graph the functions.
Lesson Planet

Exponential Functions

For Teachers 9th - 11th
Learners apply the laws of exponents as they add, subtract, and multiply exponential functions. In this algebra lesson, students identify the base and the exponent as they simplify exponential equations. They calculate the roots of...
Lesson Planet

Quiz: Exponential Functions

For Students 10th - 12th
With this quiz, high schoolers solve 10 different problems that include various exponential functions. First, they determine where the graph of a point intersects at what origin. Then, they determine the domain and range. In addition,...
1 In 1 Collection
EngageNY

Graphs of Exponential Functions

For Students 9th - 10th Standards
What does an exponential pattern look like in real life? After viewing a video of the population growth of bacteria, learners use the real-life scenario to collect data and graph the result. Their conclusion should be a new type of graph...
1 In 1 Collection
EngageNY

The Inverse Relationship Between Logarithmic and Exponential Functions

For Teachers 10th - 12th Standards
Introducing inverse functions! The 20th installment of a 35-part lesson encourages scholars to learn the definition of inverse functions and how to find them. The lesson considers all types of functions, not just exponential and...
Lesson Planet

Domain and Range for Exponential Functions

For Teachers 9th - 11th
Exceptional learners, in grades 8-10, use their algebraic know how to find the domain and range of a function. They transform a graph about a plane and define the way they find the domain and range verbally.
1 In 1 Collection
Lesson Planet

Identifying Graphs of Functions

For Teachers 8th - 12th Standards
Match the graph with its function in an exercise that focuses on variations of the graph of y = e^x. Learners are given four graphs on the same set of axes and four functions, all involving e^x. The task is to match each function with...
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Lesson Planet

How Do You Determine if a Graph Represents a Linear, Exponential, or Quadratic Function?

For Teachers 8th - 11th
What does the graph of a linear equation look like? How about a graph of a quadratic equation? What does a graph of an exponential function look like? Watch this video and see as the instructor illustrates and explains each of these...
Lesson Planet

Exponential Functions

For Students 7th - 8th
For this exponential functions worksheet, students solve and complete 20 various types of problems. First, they graph the function and state the domain and range. Then, students tell whether the graph represents exponential growth or...
Lesson Planet

Writing an Exponential Function from its Graph

For Students 9th - 12th Standards
Grow an equation for the exponential graph. Given a graph of an exponential function, class members write the equation of the function provided. The graph labels two points on the graph: the y-intercept and the point where x is one.
Lesson Planet

Linear and Exponential Functions

For Teachers 9th - 10th Standards
Provide a continuous progression to linear and exponential functions. Pupils continue to work with the discrete functions known as sequences to the broader linear and exponential functions. The second unit in a series of nine provides...
Lesson Planet

Writing an Exponential Function from a Table

For Students 9th - 12th Standards
Two points may be on the graph of an exponential function, not just on a line. Given a function table with two points, pupils determine the exponential function that contains the points. The assessment requests that learners show all...
Lesson Planet

Exponential Functions

For Teachers 9th - 11th
Students differentiate between functions and relations. In this algebra lesson, students define inverse relations and identify the inverse and coordinate pairs of equations. They graph their results on a coordinate plane.
Lesson Planet

Compare Linear and Exponential Functions

For Students 9th - 12th Standards
What is the better pay rate? The resource presents a babysitting situation with two payment plans. Pupils must determine whether to choose the linear or the exponential plan based upon the number hours of babysitting.
Lesson Planet

Compare Quadratic and Exponential Functions

For Students 9th - 12th Standards
Determine which park had the greatest attendance and when. Pupils compare the attendance at two nature parks that are modeled by a quadratic and exponential function. Scholars determine the intervals of when each park had a greater...
1 In 1 Collection
Lesson Planet

Exponential Functions

For Students 9th - 11th
In this algebra worksheet, students evaluate exponential functions using tables and graphs. There are 6 questions with an answer key.
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Functions Represented by Graphs

For Teachers 9th - 12th Standards
Graph that function! Learners explore how the shape of a graph relates to the function the graph describes. The lesson uses teamwork and Function Journals to reinforce new mathematical vocabulary.
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Comparing Functions—Exponential

For Students 9th - 12th Standards
Observe what happens when individuals change the parameters of a simple exponential function. Pupils use graphing technology to compare exponential functions while changing one parameter. The scholars then make generalizations of the...
Lesson Planet

Identifying Exponential Functions

For Students 9th - 12th Standards
Class members have the opportunity to quickly change the variables of an exponential graphs through the use of sliders on Desmos. Four graphs are given and young mathematicians, through the use of the graphing app, can discover which...
Lesson Planet

Graphing Exponentials

For Teachers 9th - 12th Standards
Bring your Algebra class to the computer lab! Using materials created by Texas Instruments, they explore exponentiasl and graphs. Be sure to download the correct materials (on the right side of the webpage) before having them walk...
Lesson Planet

Bounce Back: The Exponential Pattern of Rebound Heights

For Teachers 9th - 12th
Explore the concept of exponential functions! In this exponential functions lesson, students determine the function that represents the rebound height of a ball. They collect data on the rebound height of a ball and perform an...
Lesson Planet

Interpreting Exponential Functions

For Students 9th - 12th Standards
Given a function that models the population growth of a small town, pupils interpret the parameters of the exponential model. Scholars then find the intercept and the percentage growth factor and explain what they mean in terms of the...
Lesson Planet

Investigating Exponential Functions

For Teachers 10th - 11th
Students explore exponential function through graphing and investigating patterns of graphs. They graph exponential functions and relate these functions to real world applications of functions. Afterward, they discuss and compare peer...
Lesson Planet

Graphs and Exponential Functions

For Teachers 9th - 11th
Young scholars graph and analyze exponential functions. In this calculus lesson plan, students define the changes of the parameters and how they affect the graph. They explore asymptotes and horizontal asymptotes. They solve and graph...
Lesson Planet

Characteristics of Exponential Functions

For Teachers 9th - 12th Standards
What can an upper grader do with an exponential function? They can solve and graph it, identify its important characteristic, and differentiate graphs based on shifts in graph bases that are greater or less than one. This 45 minute...
Lesson Planet

Exponential Functions f(x) = abx

For Teachers 9th - 12th Standards
Students define exponential functions and graph the equation. In this algebra lesson, students discuss exponential growth and decay as they graph their functions. They differentiate between the base of growth and decay.
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Power Functions

For Teachers 9th - 11th
Students solve problems using algebraic exponential properties. In this algebra lesson, students write an equation given a graph of an exponential function.
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An Introduction to Exponential Functions

For Teachers 10th - 12th
Students identify exponential functions. In this algebra lesson, students rewrite word problems and solve using the properties of Exponential Functions. They graph and solve exponential equations.
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Math Regents Exam Questions: Graphing Rational Functions

For Students 9th - 12th
In this graphing rational functions worksheet, students answer 18 multiple choice problems about rational functions.  Students determine values for a which a function is undefined given the equation of the function.
Lesson Planet

Exponential Functions

For Students 9th
In this exponential functions instructional activity, 9th graders solve and complete 23 various types of problems. First, they simplify each expression. Then, students evaluate the function at different values of x and plot the ordered...
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Graphing Exponential Equations

For Students 8th - 11th
Your high schoolers will be able to relate to this exponential model. In part 1, they create a table to model a situation, plot the data, understand the domain and range, and answer questions about the general function. In part 2, they...
Lesson Planet

Graphing an Exponential Function

For Students 9th - 12th Standards
Grow your knowledge of exponential graphs. Individuals graph an exponential function on a coordinate plane given its equation. They determine whether it represents growth or decay, identify intercepts, and describe end behavior.
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Identifying Graphs of Functions

For Students 9th - 12th Standards
Take a matching problem and take challenging exponential graphs and combine to make one thought-provoking question. Learners look at four higher level exponential functions to match to the four graphs placed together. The equations and...
Lesson Planet

Exploring Function Graphs

For Teachers 9th - 11th
This is comprehensive lesson that explores different types of function graphs. Young mathematicians graph each data set, describe the characteristics of the graph, and identify the type of function represented, Students also identify the...
Lesson Planet

Transformational Graphing in the Real World: Bacteria – Growth or Decay?

For Teachers 9th - 12th Standards
Grow—not decay—your knowledge of exponential functions. Young mathematicians graph exponential functions and explore how transformations affect the graphs. They decide whether the functions represent growth or decay in the context of...
Lesson Planet

Exponential Functions

For Students 9th - 12th
In this algebra worksheet, students compute 4 functions for a given value. They graph 4 functions, and write equations for two graphs. Each function has an exponent as the variable.
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Lesson Planet

Exponential Graphs

For Students 9th - 12th Standards
Now you have the power to learn about exponential graphs. By watching a video, young mathematicians learn how to graph exponential functions. The method shown here is to create tables of values to graph equations of the form y = k^x.
Lesson Planet

Lesson 21: Exponential and Logarithmic Functions

For Students 10th - 12th
In this exponential and logarithmic instructional activity, students examine functions containing exponents and logarithms.  They identify the domain, range, asymptotes and graph the function.  This five-page instructional activity...
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Module 2: Linear and Exponential Functions

For Students 8th - 10th Standards
Write, graph, and model all things linear and exponential. Building on the previous module in a nine-part Algebra I series, learners compare linear exponential modeling. They write equations, graph functions, and analyze key features.
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Pre-Calculus Graphing

For Students 11th - 12th
In this graphing worksheet, learners solve and complete 13 various types of problems. First, they find the domain and graph writing the answer in inequality notation. Then, students describe the transformation shown and graph the figure....
1 In 1 Collection
Lesson Planet

Exponentials and Logarithms II

For Students 9th - 12th Standards
A simple question sometimes is the best for discussion. High schoolers compare a logarithmic and exponential function and composite them into one another. They graph and compare the difference between the domains. The solution contains...
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Features of Functions

For Teachers 9th - 10th Standards
What are some basic features of functions? By looking at functions in graphs, tables, and equations, pupils compare them and find similarities and differences in general features. They use attributes such as intervals of...
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Functions 11 Practice Exam

For Students 10th - 12th
Prepare for a quiz on functions with these 16 short answer and 33 extended answer questions. Questions ask test takers to describe graphs of functions, state restrictions on variables, and translate graphs of equations. They determine...
Lesson Planet

Graphs of Power Functions

For Students 9th - 12th Standards
There are parent functions, and then there are parent functions with a really interesting way to explore them. High schoolers are asked to graph different combinations of parent functions together and determine the point of intersection....
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Exponential Growth and Exponential Functions

For Teachers 8th - 12th
Students explore the concept of exponential functions. In this exponential functions lesson plan, students model exponential growth about a high school population using an applet. Students manipulate the applet to show the effect that a...
Lesson Planet

Making Money and Spreading the Flu!

For Teachers 9th - 11th Standards
Paper folding, flu spreading in a school, bacteria growth, and continuously compounded interest all provide excellent models to study exponential functions. This is a comprehensive resource that looks at many different aspects of these...
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Exponential Graph Functions

For Students 9th - 12th
In this exponential functions learning exercise, students solve and complete 13 various types of problems. First, they define what is different and what is the same about exponential and linear functions. Then, students write a rule for...
Lesson Planet

Comparing Exponential and Power Functions

For Teachers 9th - 12th Standards
Students compare and contrast exponential and power functions. For this precalculus lesson, students identify the value of x, using the graph as a visual. They compare functions with base of greater than one, to base of less than one.
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Exploring the Exponential Function

For Teachers 9th - 12th
Learners investigate exponential growth and decay.  In this exponential growth and decay lesson, students plot data on the cooling of a hot cup of coffee and the interest on a principal amount.  Learners discuss how various b-values...
Lesson Planet

Exploring Power Functions 2

For Teachers 9th - 12th Standards
Young mathematicians learn to write algebraic equations. They solve and graph different polynomial functions with different powers. They then graph radicals and identify the domain and range.
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Exponential Regression on the Ti-92/Voyage 200

For Teachers 9th - 12th
Exponential regression is the focus of this math lesson plan. Students walk through the steps of plotting exponential data on the Ti-92 and performing an exponential regression on the data.
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Function Families

For Teachers 7th - 9th Standards
Here is a solid lesson for differentiating types of functions: linear, exponential, and quadratic. Mathematicians work in groups to create a table of values for a function that they are given. They graph the assigned function and compare...
1 In 1 Collection
EngageNY

Comparing Linear and Exponential Models Again

For Students 9th - 10th Standards
Making connections between a function, table, graph, and context is an essential skill in mathematics. Focused on comparing linear and exponential relationships in all these aspects, this resource equips pupils to recognize and interpret...
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Linear vs. Exponential Functions Tasks

For Students 8th - 10th Standards
Your algebra learners will enjoy the real-life application of the three tasks presented here. They complete a table and a graph comparing the two options presented. One option is linear, while the other is exponential. After coming up...
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Murder in the First Degree - The Death of Mr. Spud

For Teachers 9th - 12th Standards
Secondary learners investigate exponential functions in a real-world scenario. They collect data on the temperature of a cooling baked potato, enter the data into lists, and graph the data using a scatter plot before finding an...
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Comparing Linear and Exponential Functions

For Students 9th - 12th Standards
Will your understanding of functions increase linearly or exponentially? Scholars compare the rates of change of a linear function and an exponential function in the context of social media messages.
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Transformations and Exponential Functions

For Teachers 10th
Tenth graders study graphing exponential functions. In this transformations lesson, 10th graders apply inquiry to determine how changes to a parent function affect its graph. Students analyze transformed graphs and generate the function...
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Exponential Graphing Using Technology

For Teachers 9th - 12th Standards
Equations can tell us a lot about graphs. Pupils begin by graphing exponential equations using technology. Based on the results, they see how different parts of the equation correspond to the graph.
1 In 1 Collection
Lesson Planet

Drawing The Inverse of Exponential Functions

For Students 8th - 12th Standards
Learners investigate the graphs of exponential functions and their inverses by using both a table of values and a graphing calculator. They apply their observations about domains, ranges, and asymptotes to generate graphs of the inverses...
1 In 1 Collection
Lesson Planet

Do Two Points Always Determine an Exponential Function?

For Teachers 9th - 12th Standards
Algebra learners explore, analyze and build an exponential equation given its form and a specific point that exists on the function in this task. The last question asks learners to apply their ideas to an exponential equation given two...
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Linear Functions: Are You Ready for the Real World?

For Teachers 9th - 11th
Here's a real-world lesson using a business simulation. Two business accounts are used to find slope and intercept functions. The class graphs and interprets the information to find a break even point. There are plenty of worksheets and...
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Two Points Determine an Exponential Function II

For Teachers 9th - 12th Standards
Your algebra learners will build an exponential equation given a graph with two specific points labeled. 
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Classifying Functions-Grade 11

For Teachers 10th - 11th
Investigate non-linear functions based upon the characteristics of the function or the representation of the function. The functions are displayed in multiple formats including as graphs, symbols, words, and tables. Learners use written...
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Extra Practice 48: Graphing Exponential and Logarithmic Functions

For Teachers 10th - 12th
In this graphing worksheet, students graph exponential and logarithmic functions. A coordinate plane is provided for each problem. Eighteen problems are on this two-page worksheet.
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Exponential Functions

For Students 9th
In this exponential functions worksheet, 9th graders solve and complete 10 different problems. First, they graph each function and state the y-intercept. Then, students use the graph to determine the approximate value of the given...
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Graphing Polynomial Functions

For Students 11th
In this algebra worksheet, 11th graders graph polynomial functions using quadratics and other exponential functions. They identify the vertex and other properties of a parabola. There are 8 problems with an answer key.
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Test 2: Rationals, Exponentials, and Logarithms

For Students 9th - 12th Standards
Running out of logarithm questions in class? The nicely organized two-page worksheet provides practice in rational, logarithmic, and exponential functions. All the topics include graphing, solving, and finding domain and range. 
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The Natural Exponential Function

For Students 11th - 12th Standards
Ready to apply the concepts related to the natural exponential equations and logarithmic equations? A math lesson reviews concepts from inverse properties to solving to derivatives and integrals. 
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Linear Piecewise Functions

For Teachers 10th - 12th
Students explore the concept of piecewise functions. In this piecewise functions lesson, students graph piecewise functions by hand and find the domain and range. Students make tables of values given a piecewise function. Students write...
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Module 4: Linear and Exponential Functions

For Teachers 8th - 10th Standards
Sequences and series are traditionally thought of as topics for the pre-calculus or calculus class, when learners are figuring out how to develop limits. But this unit uses patterns and slopes of linear functions in unique ways to bring...
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Writing Exponential Functions Based on Data

For Students 9th - 12th Standards
Give your class a concrete example of exponential growth and decay using this hands-on activity. These Algebra II lessons allow for the exploration of exponential growth and decay models, as well as the discovery of the patterns of each....
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Business Management and Administration: Compound Interest - A Millionaire's Best Friend

For Teachers 6th - 12th Standards
Many math concepts are covered through this resource: percentages, decimals, ratios, exponential functions, graphing, rounding, order of operations, estimation, and solving equations. Colorful worksheets and a link to a Google search for...
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Eight Special Functions and Their Graphs

For Students 9th - 12th Standards
Do you know what your graph is supposed to look like based on the equation? Knowing a parent function and its associated graph makes problem solving easier when transformations are included. Each function has two problems that...
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Exponential Decay: Cool Sunglasses

For Students 10th - 12th Standards
Who wouldn't want to wear four pairs of sunglasses? Each pair of sunglasses reduces the percent of incoming light by one-half. An interactive tutorial helps young mathematicians build a graph that models this scenario. They then explore...
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Library of Functions

For Students 9th - 12th Standards
Join the family picnic and see how all the functions come together in a PowerPoint that highlights their main features. As it includes topics such as domain, range, and intercepts, the slides are a great guide to promote class discussions. 
1 In 1 Collection
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Exit Ticket: Graphs of Functions

For Students 9th - 11th Standards
This worksheet is designed as an exit ticket for a lesson on graphs of functions. Learners apply their knowledge of general behavior of functions to match seven equations with their graphs. Function types include linear, quadratic,...
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Functions

For Students 11th
In this functions worksheet, 11th graders solve and complete 21 various types of problems related to different functions. First, they graph each of the equations given and create a table of values, labeling the asymptote. Then, students...
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The M & M Function

For Students 8th - 11th Standards
In this M & M worksheet, students perform probability experiments.  They collect and interpret data, identify the exponential function describing the data and create graphs from the collected information.  This one-page worksheet...
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Functions Represented by Tables

For Teachers 9th - 12th Standards
So many functions and so little time! Beginning learners investigate different types of functions through independent practice and collaboration with others. The lesson uses real data and cross-curricular ties to science.
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Discovering Different Types of Functions

For Teachers 10th - 12th
Graph polynomials and identify the end behavior of each polynomial function. The class differentiates between linear, quadratic, and other polynomial equations.
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Functions Represented by Situations

For Teachers 9th - 12th Standards
What good are functions in the real world? Learners take real-world situations and investigate the associated function. Documentation of real-world scenarios helps learners connect key mathematical vocabulary words with certain functions.
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Graphs and Functions

For Teachers 8th - 10th
Use this series of activities to introduce learners to graphing functions. They graph both linear and quadratic equations by hand and with a Graph Sketcher Tool. Several imbedded links and handouts are included in the lesson.
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Basic Graphs that Every Algebra Student Should Know!!

For Teachers 7th - 12th
A narrator shows us what some basic graphs are and the equations that produce certain graphs. He does not actually explain how to graph but simply shows different types of graphs.
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Exponential Modeling

For Teachers 10th - 12th
Investigate exponential growth and decay. A set of six activities has pupils collecting and researching data in a variety of situations involving exponential relationships. They model these situations with exponential functions and solve...
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Linear and Exponential Change: Comparing Growth Rates

For Teachers 8th - 10th Standards
This thirteen-page PowerPoint presentation guides geometry learners in interpreting linear functions, linear data and their trend lines, the consequences of their constant rate of change, and growth rate. Real-life models including...
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Two Points Determine an Exponential Function I

For Teachers 9th - 12th Standards
Learners construct an exponential function from a graph, and two given points on the graph, as they analyze what makes up an exponential function.
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Comparing Linear and Exponential Representations

For Teachers 7th - 9th Standards
Graphs, tables, and equations, oh my! Your Algebra learners will compare and contrast linear and exponential functions in this complete lesson plan. It includes the graphs, tables, verbal description scenarios, equations, and an...
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Exponential Growth versus Linear Growth II

For Teachers 9th - 12th Standards
Your algebra learners discover that exponential functions, with a base larger than one, outgrow linear functions when the inputs increase sufficiently. Their analysis includes using a graphing calculator to produce tables.
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Linear and Exponential Models

For Teachers 9th - 12th Standards
How many people did you say? An instructive instructional activity uses human population growth to explore linear and exponential functions. Learners work cooperatively to use real-world population data and apply concepts of models.
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Exponentials

For Teachers 9th - 12th Standards
Algebra scholars read about and practice problems involving exponents. They solve problems by using common exponential rules for multiplying and dividing exponents. They use prior knowledge of logarithms to solve exponential problems....
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Function Flyer

For Students 8th - 12th Standards
Fly through graphing functions with the Function Flyer. Young mathematicians use an interactive to graph different types of functions. A set of exploration questions has users investigate patterns in functions.
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Saxon Math: Algebra 2 (Section 9)

For Teachers 9th - 12th Standards
Section 9 of the 12 linked Saxon Math sections introduces the young algebrist to graphing periodic functions, creating graphs from quadratic roots, working with inequalities, and rational equations. Common among all the lessons is the...
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Function Presentations (Unit Assessment)

For Teachers 9th - 12th Standards
Present the world to me! Participants develop presentations about functions they learned through research. They then share their ideas about how functions apply to global warming with the class.
2 In 2 Collections
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Parent Functions Review Sheet

For Students 9th - Higher Ed Standards
No laundry or cooking dinner here: these parent functions are all about math. Every graph you could think of from basic linear functions to the hyperbolic arccotangent function are included. With 40 parent functions, the worksheet can be...
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How to Recognize the Type of Graph from a Table

For Teachers 8th - 10th Standards
Linear, quadratic, and exponential functions are represented only by their table of values in this simple, well-written worksheet. Learners decide the type of graph represented based on the differences in the function values. Included is...
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Logarithmic Functions

For Students 10th - Higher Ed
In this math worksheet, students write the following logarithms as exponentials. They also use the example to help graph the exponential functions.
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Exponential Population Growth

For Students 10th - 12th
In this exponential population growth learning exercise, students read word problems and determine the exponential growth of a specified populations.  They find the percent of growth and compute exponential regressions.  Students graph...
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Lesson #45 Graphs of Logarithmic and Exponential Functions

For Teachers 11th - 12th
Students investigate exponential and logarithmic functions.  In this Pre-calculus/Calculus lesson, students investigate the relationship between y = ln(x) and y = e^x.  Students graph the functions and show they are inverses of each other. 
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Exponential Growth

For Teachers 9th - 12th
Young scholars explore the concept of exponential functions.  In this exponential functions lesson, students examine the behavior of exponential functions when the base is between 0 and 1.  Young scholars discuss what would happen to the...
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NUMB3RS Activity: Exponential Modeling

For Teachers 10th - 12th
Students investigate exponential functions.  In this Algebra II/Pre-calculus lesson students find an exponential model from a set of data.  Students investigate the affects of changing parameters have on the graph of an exponential...
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Function Operations

For Teachers 9th - 12th Standards
How on earth do functions explain climate change? Classroom discussion ties global warming and climate change to functions. Learners practice skills using function notation before groups compete in a game.
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Functions

For Teachers 9th - 12th Standards
A function is like a machine that has an input and an output. Challenge scholars to look at the eight given points and determine the two functions that would fit four of the points each — one is linear and the other non-linear. The...
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Exponential Growth and Decay

For Students 8th - 10th
Quiz your middle and high schoolers on solving exponential growth and decay. First, they evaluate for a variable given the second variables value. Then, they graph an equation that illustrates the exponential growth or exponential decay...
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Exploring Exponential Graphs

For Students 9th - 10th Standards
Using a graphing calculator, your algebra 2 learners compare and contrast parent exponential graphs with their transformations. Range, horizontal asymptotes, y-intercepts and general graph changes are some of the characteristics the...
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Rate of Change

For Students 8th - 10th Standards
Get your classes moving and collaborating! The activity moves learners through a set of four stations. Each station presents a linear and/or exponential function task. Ultimately, learners compare linear and exponential functions and...
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Module 1: Functions and Their Inverses

For Students 9th - 12th Standards
Nothing better than the original! Help your class understand the relationship of an inverse function to its original function. Learners study the connection between the original function and its inverse through algebraic properties,...
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Skeeters Are Overrunning the World

For Teachers 8th - 10th Standards
Skeeters are used to model linear and exponential population growth in a wonderfully organized lesson plan including teachers' and students' notes, an assignment, graphs, tables, and equations. Filled with constant deep-reaching...
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Exploring the Exponential Function

For Teachers 9th - 12th Standards
Learners collect and analyze data regarding exponential functions of the form y = abx.  Students explore the affects of changing parameters on the graph of the function. 
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Comparing Linear and Exponential Functions

For Teachers 9th - 12th Standards
Teach your class how to differentiate between linear and exponential functions. They use exponential properties to solve problems, graph them using the TI-Navigator, and make comparisons.
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Power Functions

For Teachers 7th - 9th
Young scholars identify the different properties of exponential functions. In this algebra lesson, students graph and analyze exponential functions as it relates to growth and decay. They apply the laws of exponents to add, subtract,...
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Exponential Equations and Functions

For Teachers Higher Ed
In this college level Pre-Calculus worksheet, students solve problems involving exponential functions.  Students determine the domain, range, y-intercept and asymptotes of exponential functions. The three page worksheet contains seventy...
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Viral Marketing

For Teachers 9th - 12th Standards
What is "viral marketing" and how does it relate to mathematics? Young mathematicians use exponential functions to develop a mathematical model for a business advertising campaign. Learners then see how their campaigns increase...
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Piecewise Defined Functions

For Teachers 9th - 11th Standards
Graph piecewise functions as your learners work to identify the different values that will make a piecewise function a true statement. They identify function notations and graph basic polynomial functions. This lesson includes a series...
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Linear and Exponential Models

For Teachers 9th - 12th
Students investigate the differences between linear and exponential models.  For this linear and exponential models lesson, students make a table of given data.  Students determine if the data is linear or exponential by plotting the...
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Exponential Functions

For Teachers 9th - 12th Standards
Your algebra learners analyze and interpret the general form and the graph of two functions. The increase of the function due to the multiplicative factor is emphasized.
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Sorting Functions

For Teachers 9th - 12th Standards
Graph A goes with equation C, but table B. The short assessment task requires class members to match graphs with their corresponding tables, equations, and verbalized rules. Pupils then provide explanations on the process they used to...
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Functions Represented by Equations

For Teachers 9th - 12th Standards
Who knew there were so many types of functions? Pupils investigate several types of functions through discussion and peer presentations. Function journals assist learners to document their progress.
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Function Family Fun

For Teachers 9th - 12th Standards
It's time for a family reunion—function families, that is. Pupils first review different types of parent functions. They then see how to apply transformations to graphs and learn how to select the most appropriate type of function to...
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Charging Up, Charging Down: Exponential Models

For Teachers 10th - 12th
Students collect and analyze voltage data. In this math lesson plan, students investigate exponential functions using the TI and a Voltage Probe. They graph their data and analyze it using a table.
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Graphs of Power Functions

For Teachers 8th - 12th Standards
This activity consists of three exercises in which learners sketch the graphs of various power functions on the same axes. They use their sketches to make comparisons and observations which lead to generalizations about the graphs of...
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Exponential Transformations

For Teachers 9th - 12th Standards
Perform transformations on exponential functions! Teach your class how to perform dilation, compression, and translation. They graph exponential functions using the TI Calculator.
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National Debt and Wars

For Teachers 9th - 12th Standards
Take a functional approach to the national debt. Learners collect information about the national debt by decade and plot the data. They determine whether an exponential curve is a good fit for the data by comparing the percent changes...
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Analyzing a Graph

For Teachers 9th - 10th Standards
Collaborative groups utilize their knowledge of parent functions and transformations to determine the equations associated with graphs. The graph is then related to the scenario it represents. 
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Exponential Decay Exploration

For Teachers 9th - 11th Standards
How can you model exponential decay? Explore different situations involving exponential decay functions and decreasing linear functions by performing activities with MandM candy, popcorn kernels, and number cubes.
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Transformations of Linear and Exponential Graphs

For Students 8th - 10th Standards
Your transformers will create and analyze graphs to discover which operations produce which transformations. Linear and exponential functions are used to model the transformations.
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Algebra II: Make Sense of Problems Using Exponential and Logarithmic Functions

For Teachers 9th - 12th Standards
You'll have more problems than solving an exponential equation if your town's population decreases to zero. Individuals create an equation to represent the population of a town given information verbally. Using logarithms, they solve for...
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Relationships Between Quantities and Reasoning with Equations and Their Graphs

For Teachers 6th - 10th Standards
Graphing all kinds of situations in one and two variables is the focus of this detailed unit of daily lessons, teaching notes, and assessments. Learners start with piece-wise functions and work their way through setting up and solving...
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Newton’s Law of Cooling

For Students 9th - 10th Standards
As part of an investigation of transformations of exponential functions, class members use Newton's Law of Cooling as an exponential model to determine temperature based on varying aspects. The resource makes comparisons between models...
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King for a Day

For Students 9th - 12th Standards
Rumor has it exponential functions help solve problems! In a kingdom filled with rumors, young scholars must determine the speed a rumor spreads. The ultimate goal is to decide how many people must know the rumor for it to spread to the...
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Representing Functions of Everyday Situations

For Teachers 10th - 12th Standards
Functions help make the world make more sense. Individuals model real-world situations with functions. They match a variety of contexts to different function types to finish a helpful resource.
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The “WhatPower” Function

For Teachers 9th - 12th Standards
The Function That Shall Not Be Named? The eighth installment of a 35-part module uses a WhatPower function to introduce scholars to the concept of a logarithmic function without actually naming the function. Once pupils are comfortable...
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Identifying Even and Odd Functions

For Students 9th - 12th Standards
Is it even ... or odd? The task provides four functions to identify as being even, odd, or neither. Pupils use algebraic methods to make their decisions with select exponential, quadratic, and cubic functions.
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Quiz 2: Types of Functions

For Students 9th - 12th Standards
Here is a resource that provides the structure of an assessment with the convenience of a full answer key. The focus is on rational, exponential, and logarithm functions with a few questions on solving polynomials. 
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Exponential Functions

For Students 11th
In this exponential functions worksheet, 11th graders solve and complete 22 different types of problems. First, they sketch the graph of each function and state the function's domain and range. Then, students determine whether each...
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Exploring Exponential Growth and Decay Functions

For Teachers 9th - 11th
Students differentiate between exponential growth and decay. For this algebra lesson, students solve exponential equations using properties of exponents. They use the Ti calculator to graph and analyze their functions.
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Intersecting Graphs

For Teachers 9th - 10th
Ninth graders know how to solve a system of linear equations, but what happens when the system involves an exponential function? The instructional slideshow teaches viewers to determine solutions to systems of equations with linear and...
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Powers and Roots as Inverses-ID: 9826

For Teachers 11th
Texas Instruments has composed yet another lesson to get your class using the TI-Inspire calculator to solve power and root functions. They find similarities and differences in the graphs of even and odd power and root functions then...
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Module 2: Logarithmic Functions

For Students 9th - 12th Standards
Build a solid understanding of logarithmic functions and equations. Five lessons in the module begin by developing the concept of a logarithm. The next lessons address graphing logarithmic functions, logarithmic properties, and solving...
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The Calcumites are Coming!

For Teachers 9th - 12th
Students explore the concept of population growth. In this population growth lesson, students graph the population growth of a 'calcumite' which is a made up species whose population grows exponentially. Students plot the data over the...
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Linear, Exponential, and Quadratic Models: Bernoulli Effect

For Students 10th - 12th Standards
How can an object as heavy as an airplane fly? Turns out the answer is quadratic! Your classes explore the Bernoulli Effect through an interactive graph representation. As a plane increases in speed, the lift force also increases. Young...
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Exponential Growth

For Teachers 7th - 9th
Young scholars study exponential functions. In this exponential growth lesson, students conduct a simulation in which a population grows at random but predictable rate. Young scholars compare and contrast linear and exponential...
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Polynomial, Rational, and Exponential Functions Challenging Group Worksheet

For Students 11th - Higher Ed
In this polynomial function, rational function, and exponential function review worksheet, students answer twelve challenging problems.  This worksheet is designed to be done in groups and not expected to be finished.
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Drawing Inverses

For Teachers 9th - 12th Standards
An Algebra II instructional activity draws the connection between the exponential function and its inverse. By graphing an exponential function and using tables and a calculator, young scholars graph the logarithmic function. The plan...
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Basketball Rebounds

For Teachers 9th - 12th Standards
Your young basketball players will build a table and develop a general formula for a decaying exponential scenario involving the rebound distance of a bouncing ball. Using a CBR and graphing calculator can make this even more hands-on...
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Betweenness IV

For Students 11th - 12th Standards
Challenge your classes to think between the curves. Given two function formed by the combination of two exponential functions, individuals must write three functions in which all values would lie between the given. The question is...
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Graphs (2006)

For Teachers 9th - 12th Standards
When told to describe a line, do your pupils list its color, length, and which side is high or low? Use a worksheet that engages scholars to properly label line graphs. It then requests two applied reasoning answers.
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Unit Plan: Exponential and Logarithmic Functions

For Teachers 10th - 12th Standards
A six-day unit for algebra II on exponential and logarithmic functions builds upon Chapter 12 of Merrill Algebra II with Trigonometry; Applications and Connections. The text provides assistance in the depth of instruction and homework...
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Geometric Transformations Applied to Function Families

For Teachers 9th - 12th Standards
Transform your life with functions! Learners explore geometric transformations of functions with group activities. Guided math journaling and individual practice ensure success with difficult concepts.
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Recognizing the Connections among Function Representations

For Teachers 9th - 12th Standards
Functions are all fun and games! The lesson stealthily disguises a formative assessment as an entertaining card game. Learners must use their knowledge to make connections among different representations and the related functions.
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Graphing and Properties of Quadratic Functions

For Students 6th - 11th Standards
Summer projects are key to helping leaners stay proficient in math skills. Here is a project that reinforces Algebra II skills. Including five parts, the project explores graphing functions and quadratic equations such as the standard...
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Exponential Functions: Half Life and Doubling Time

For Teachers 9th - 12th
Learners investigate the concept of exponential functions and how they increase in size over time. They simplify the functions in order to find the solutions that are possible and perform analysis of the curved line that is produced when...
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Exponential Reflections

For Teachers 11th
Eleventh graders explore exponential functions.  In this Algebra II lesson, 11th graders investigate the reflection of an exponential function and the inverse of y = ex.
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Continuous Growth and the Number e

For Teachers 9th - 11th
Learners differentiate between exponential growth and decay. In this algebra instructional activity, students identify the continuous growth rate of a function. They relate growth, continuous growth and decay to Euler's number.
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Module 3: Polynomial Functions

For Students 9th - 12th Standards
An informative module highlights eight polynomial concepts. Learners work with polynomial functions, expressions, and equations through graphing, simplifying, and solving. 
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Reading Graphs

For Teachers 7th - 10th
Working independently or in teams, your class practices connecting graphs, formulas and words. This instructional activity includes a guided discussion about distance vs. time graphs and looking at how velocity changes over time.  
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Family Ties

For Teachers 8th - 12th Standards
They say it runs in the family. Small groups use a card sorting activity to group graphs of functions into families. After grouping by families, the class develops conclusions for parent functions and create a graphic organizer.
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Functions: Domain, Range, End Behavior, Increasing or Decreasing

For Students 9th - 12th Standards
Examine key features of various functions through exploration. A comprehensive activity has learners describe the domain, range, end behavior and increasing/decreasing intervals of various functions. Function types include linear,...
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Module 2: Logarithmic Functions

For Students 10th - 12th Standards
You can't build a fire with these logs! Filled with hands-on investigations, a complete logarithmic unit offers both instruction and practice. Learners first build an understanding of the new function, then explore properties before...
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Average Rate of Change

For Teachers 8th - 10th Standards
Learners investigate average rates of change for linear functions and connect the concept to slope. They then determine average rates of change in quadratic and exponential functions.
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6 Billion and Counting

For Teachers 9th - 12th Standards
Will all the people be able to fit? Using historical population growth rates for continents, pupils determine estimates for the future population. The second day, pupils investigate whether a linear, quadratic, or exponential function...
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Piecewise Modeling with Multiple Functions: Federal Debt

For Teachers 9th - 12th
Learners analyze data on debt and write an equation. In this statistics lesson, students are given data from different time periods, and are asked to graph and analyze the data. They work in groups, and are assigned different parts of...
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Differentiation of Polynomials and Exponenital Functions

For Students 11th - Higher Ed
Extend pupil understanding of derivatives and tangent lines. The problem presented asks individuals to find the points on a graph that have a tangent line parallel to a given line. The instructor shows how to use the concept of a...
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Exponential Decay Functions

For Students 7th - 8th
In this exponential functions worksheet, students solve and complete 13 various types of problems. First, they state whether the table represents an exponential function or not and why. Then, students graph each function and identify its...
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Graphing at all Levels: It's a Beautiful Thing!

For Teachers 8th - 12th Standards
Mixing math and art is done in this lesson by applying graphing knowledge to create a unique piece of art. This lesson varies acording to the graphing knowledge of the artist. First, learners identify and review various types of graphing...
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Exploring Exponential Models

For Students 11th Standards
Explore the difference between exponential growth and decay with this worksheet. Use tables, graphs, and algebraic methods to gain insight. The notion of an asymptote is also introduced. 
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Exploring Power Functions 1

For Teachers 9th - 12th Standards
Learners describe the end behavior of polynomial functions. Pupils relate the behavior of the graph to the exponent of the graph. They differentiate graphs with odd-exponent and graphs with even exponents.
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Exponential Functions and the Natural Logarithm

For Teachers 8th - 12th Standards
Students solve exponential and log functions. For this algebra lesson, students graph natural log and logarithmic functions. They compare and contrast between logs and the exponential graphs. 
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Domain and Range of Exponential Functions

For Teachers 9th - 12th Standards
Have your class find the domain and range for each function. High schoolers graph equations using the TI. They find all the x and y values as they relate to the domain and range.
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Exponential Growth

For Teachers 9th - 12th Standards
Learners differentiate between growth and decay, of each function by graphing and solving exponential and logarithmic functions. 
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Linear and Exponential Models—Comparing Growth Rates

For Students 9th - 10th Standards
Does a linear or exponential model fit the data better? Guide your class through an exploration to answer this question. Pupils create an exponential and linear model for a data set and draw conclusions, based on predictions and the...
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Solving Exponential Equations

For Teachers 10th - 12th Standards
Use the resource to teach methods for solving exponential equations. Scholars solve exponential equations using logarithms in the twenty-fifth installment of a 35-part module. Equations of the form ab^(ct) = d and f(x) = g(x) are...
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Interpreting Tables and Graphs

For Teachers 9th - 12th Standards
Intrigue learners by showing them that they can help save the planet—using math! Participants evaluate environmental data presented in tables and graphs. They must use the data to write a newspaper article in order to share the...
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Exponential and Logarithmic Functions

For Students 9th - 12th Standards
High schoolers grow their skills exponentially after completing this thorough worksheet. Going from simple to difficult, it hits all the major skills regarding exponential and logarithmic functions including simplifying, solving,...
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Solving Equations by Using Functions

For Teachers 9th - 12th Standards
How can you find a solution to a function using a graph? Learners explore solving functions with graphs. Cooperative learning and math journaling assist class members when exploring several types of functions.
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Modeling a Context from a Graph

For Teachers 9th - 10th Standards
Using the modeling cycle, collaborative pairs develop functions that model a graph from a context. They then analyze their function models in order to answer questions about the scenario. 
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Module 1: Functions and Their Inverses

For Students 10th - 12th Standards
Undo a function to create a new one. The inverse of a function does just that. An inquiry-based lesson examines the result of reversing the variables of a function, beginning with linear patterns and advancing to quadratic and...
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Comparing Multiple Representations of Functions

For Students 8th - 10th Standards
Graphs, tables, and equations, oh my! Pupils tackle a set of questions using given information in different representations. The three activities each have a different goal. The first compares the same linear relationship using different...
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Module 3: Features of Functions

For Students 8th - 10th Standards
Learn how to represent functions in multiple ways. Learners analyze functions as equations, graphs, and verbal descriptions. The analysis includes intercepts, behavior, domain, and range. The module of seven lessons makes up the third...