Graphing Functions Teacher Resources

Find Graphing Functions lesson plans and worksheets
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High School Math Handouts

For Teachers 8th - 12th Standards
A collection of different resources can augment any math curriculum. Sheets can be printed, posted on the wall, or emailed to students for use in the classroom.
3 Items in Collection
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"Grade 8, Claim 2 & 4: Problem Solving & Communication Reasoning Supports"

For Teachers 8th Standards
Prepare eighth-graders for the Smarter Balanced Assessment with a small but powerful collection of three resources comprised of teacher and student-friendly slides that review key concepts in the eighth grade standards. Claim 2 focuses...
10 Items in Collection
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Grade 8, Claim 1: Concepts and Procedures Item Slide Shows

For Teachers 8th Standards
Ten resources make up a collection of student and teacher-friendly slides that prepare eighth graders for the Smarter Balance assessment. Learners review rational and irrational numbers, convert repeating decimals to fractions, as well...
35 Items in Collection
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Algebra: High School Common Core Math

For Teachers 9th - 12th Standards
All Algebra, all the time! Here is a compiled list of resources that address all of the standards regarding Algebra Common Core for high school. Each resource has the main standard it addresses under the notes section of the item. 
12 Items in Collection
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EngageNY Grade 8 Math Module 5: Examples of Functions from Geometry

For Teachers 8th Standards
A collection of 11 lessons boost eighth-graders' knowledge of geometric functions. Scholars delve deep into the concept of a function—the definition, examples, graphing and comparing. Learners explore the volume of cubes and cylinders....
5 Items in Collection
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Graphing Rational Functions

For Teachers 9th - 12th
With the many steps involved in graphing rational functions, your learners may need a little extra help before they get the hang of it. Here are some supplement notes and practice problems to support your class as they investigate this...
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Graph Functions: English Learners

For Students 6th - 11th
In this ELL, graphing functions activity, students solve 1 word problem where they write an equation, create a table of values, plot the points and a graph and draw a graph of the function. Step-by-step instructions and scaffolding are...
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Algebra : Graph Functions

For Students 8th - 12th
For this graphing functions worksheet, learners examine 3 graphs of functions. Students then answer 5 problems where they match the graph to an equation, create a graph based on a set of ordered pairs or answer questions based on the...
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Algebra: Graph Functions

For Students 8th - 11th
In this graphing functions worksheet, learners solve 10 problems where they create a table of values then make a graph for a given function.
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Graphing Functions

For Students 8th Standards
How do letters and numbers create a picture? Scholars learn to create input/output tables to graph functions. They graph both linear and nonlinear functions by creating tables and plotting points. 
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2D-Graphing Functions

For Teachers 8th - 10th
Practice graphing basic equations. Algebra learners complete a table showing values of x and y. They graph the results on a coordinate grid. There are six problems: three equations are linear, and three are quadratic. The "show your...
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Quick-Draw McGraw

For Students 10th - 12th
High schoolers graph functions that are given, and then they write the equations for the completed graphs. There are several problems included, and they are designed to be used without calculators.
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2D - Graphing Functions #5

For Students 8th - 10th
Perfect for Algebra 1, this simple graphing functions worksheet, requires learners to find the slope and y-intercept of a linear equation and graph equations. This resource is two-pages long and contains 6 multi-step problems.
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Graphing Functions

For Students 10th
In this graphing functions worksheet, 10th graders solve 10 different problems that illustrate various graphs of functions. They determine the type of function that each graph shows. Then, students write the equation for the line graphed...
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Algebra: Graph Functions: Homework

For Students 6th - 7th
In this graph functions worksheet, students review the example box for the graph of function y=3x. Students review how to plot and connect the points, extend the line segments, and find the point. Students then use the table and plotted...
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Graph Functions: Problem Solving

For Students 6th - 7th
In this graph functions worksheet, learners use their knowledge of graph functions to problem solve and complete the five questions.
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SAT Prep: Test 5 Section 3 Part 4

For Students 9th - 12th
Explaining that the only thing he gets in return for these videos "is the satisfaction of you guys getting a perfect score on the SAT," Sal charges on through the practice SAT problems. Students who have a difficulty with parabolas and...
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SAT Prep: Test 1 Section 6 Part 4

For Students 9th - 12th
Number 11 in the practice section of The Official SAT Study Guide begins with finding the perimeter of a given triangle. Once students solve this multiple-choice question, they can find ways to solve the additional problems on the page,...
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Worksheet Three: Graphing Functions

For Students Higher Ed
In this graphing functions instructional activity, students plot inequalities, and graph given functions. They use their graphing calculator to solve problems. This two-page instructional activity contains 8 multi-step problems.
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Function Graphing--ID: 8252

For Teachers 9th
Those graphing calculators can be tricky; good thing Texas Instruments has devised a lesson on how to use their TI-Nspire calculator to graph functions. Kids investigate functional notation as they graph ordered pairs in the form (a,...
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Sound Loudness

For Teachers 9th - 11th
Investigate sound through non-linear functions, graphing, function tables, and equations. The class is given a graph of sound vs. distance, they must determine an equation to fit the graph and knowing that the graph is not linear....
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Hybrid Vehicles: Cut Pollution and Save Money

For Teachers 7th - 8th
Math and science meet in this lesson on hybrid electric automobiles. This 24-page resource provides everything you need for teaching a lesson that compares the use of internal combustion engines to hybrid electric engines. Participants...
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Graph Functions: Practice

For Students 6th - 7th
For this graph functions worksheet, students complete several activities to help them graph functions. Students use the table and the graph to complete the questions. Students also answer two test prep questions.
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Graph Functions: Reteach

For Students 6th - 7th
In this graph functions worksheet, students review the box with the graph and its various functions. Students then use the gird and the table to answer the questions.
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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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Graphing Functions

For Students 8th - 10th
In this graphing functions worksheet, students enter functions into a graphing calculator and observe the resulting graphs.  They graph functions by hand and label the coordinate plane.  This four-page worksheet contains instructions for...
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Graphing Functions

For Teachers 9th - 12th
Students graph linear, quadratic, absolute value, and square root functions using transformations. In this graphing functions lesson plan, students are provided a worksheet.
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Tables and xy-Coordinates

For Students 7th - 9th
Use this graphing functions worksheet to have learners complete four tables and graph the results on the included coordinate grid.
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Graphing Functions by Plotting Points - Quadratic

For Students 8th - 11th Standards
Watch as your knowledge of quadratic functions grows parabolically. An educational video shows scholars how to graph quadratic functions. The method shown here is to create a table of values and graph the function by hand.
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Graphing Functions by Plotting Points - Linear

For Students 8th - 11th Standards
It's a straight line to understanding how to graph linear functions. Scholars watch an informative video to learn the process of graphing linear functions. They understand how to make and fill in a table of values and then plot the...
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Graphing Functions by Plotting Points - Constant

For Students 8th - 11th Standards
Are you constantly having trouble with constant functions? Learn how to graph these types of functions by watching a helpful video. Viewers follow along as the narrator creates a table of values and plots the resulting points to graph...
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Graphing Functions Worksheets

For Students 9th - 11th
Get out the graph paper; it's time to graph functions! Upper graders solve and graph 10 different problems that include graphing polynomial functions, finding the bounds for x and y that display the basic characteristic of the graph of...
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Test 1: Graphing Functions

For Students 9th - 12th Standards
Graph the night away with all the different types of functions provided in the worksheet. Linear, quadratic, and rational all ask for graphs, domain and range and other key factors about the functions.
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Graphing Functions

For Students 9th - 11th
In this graphing functions learning exercise, students solve and complete 13 different problems that include identifying and graphing various functions. First, they graph each of the functions shown on the graphs provided. Then, students...
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F(x)g(x): A Tale of Two Functions

For Students 10th - 12th
In this graphing functions instructional activity, students solve four problems where they graph given functions, find the sum related to the area under the curve and determine an integral.
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Graphing Functions

For Students 11th - Higher Ed
In this graphing functions worksheet, learners solve and complete 25 various types of problems. First, they evaluate each of the limits presented. Then, students graph each given function, graphing both the equation and then the...
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Combining Functions

For Teachers 11th
This worksheet includes 46 problems for students to solve. They must combine, solve, and graph functions, and use functions to evaluate and solve equations. This would be an excellent exam or pre test.
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Algebra: Graph Functions practice 13.4

For Students 5th - 6th
For this graphing functions worksheet, students make a table of values, graph the functions, and tell whether the ordered pair lines are on the lines. Students solve eight problems.
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Graphing Functions

For Students 11th
In this graphing functions learning exercise, 11th graders solve and complete 10 different types of problems. First, they graph each function and list the asymptote, domain and range for each. Then, students sketch each graph. They also...
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Graphing Functions

For Students 9th - 12th
For this graphing functions worksheet, high schoolers write functions in logarithmic and exponential forms.  They evaluate logarithms and determine the inverse of a function.  Students graph functions.  This six-page worksheet contains...
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Graphing Functions

For Students 11th - Higher Ed
In this graphing functions learning exercise, students solve and complete 16 various types of problems. First, they evaluate each of the limits provided. Then, students graph each of the functions and their asymptotes as given.
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Modeling a Basketball Throw

For Teachers 9th - 12th
Play ball! High schoolers explore the concept of quadratic equations through modeling how shooting a basketball can be expressed as a quadratic function. They impose a coordinate grid on the path of a shooting basketball and determine...
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Fill 'er Up

For Teachers 6th - 8th
Designed for middle schoolers, this math resource requires learners to pour liquid into a variety of containers. They keep track of the amount of water poured in, the height of the water in the container, and they plot this information...
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Graphing Functions

For Students 11th - Higher Ed
In this graphing functions worksheet, students explore the graph of a function consisting of two line segments. They find the values in the open interval under given conditions. Students graph the closed interval. This two-page worksheet...
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10-4-10 Quiz: Graphing Functions

For Students 9th - 12th
In this graphing functions worksheet, high schoolers graph 3 problems  Students determine axis of symmetry, intercepts, domain, range, etc. of functions.
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Graphing Functions

For Students 11th
For this graphing functions worksheet, 11th graders solve and complete 15 different types of problems. First, they sketch a graph of each function. Then, students find the interval on which the variable is increasing, decreasing, or is...
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Graphing Functions

For Students 11th - Higher Ed
In this graphing functions activity, students solve and complete 76 various types of problems. First, they draw the graph of the functions and find the domain and range for each. Then, students write a piecewise formula for the...
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Reading Graphs

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

For Teachers 7th - 9th Standards
Middle schoolers describe plotting functions on the Cartesian coordinate plane. They solve functions on paper and using an online tool to plot points on a Cartesian coordinate plane creating lines and parabolas.
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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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Graphing 9 Basic Functions

For Students 8th - 11th Standards
Graphing functions by hand is pretty easy. A comprehensive video reviews how to graph different function types. It looks at the constant, identity, quadratic, cubic, absolute value, square root, cube root, reciprocal, and squared...
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Smarter Balanced Sample Items: High School Math – Target M

For Students 9th - 12th Standards
Your knowledge of graphs is a function of how much you try. Young mathematicians work on a set of 12 questions that covers graphing functions, comparing functions, and rewriting functions in different forms to determine key features....
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Graph Sketcher

For Students 9th - 12th Standards
Sketch graphs with the Graph Sketcher. Scholars graph functions on a coordinate plane. An interactive makes it as easy as inputting the function and clicking a button.
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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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Graphit

For Students 5th - 12th Standards
No graphing calculator? No worries, there's an app for that! Young mathematicians use an app to graph functions. In addition, they can also plot data points.
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Problem Solving: Graphing Functions

For Students 5th - 6th
In this graphing functions worksheet, students solve 6 word problems, finding ordered pairs, missing coordinates and numbers, slopes of lines and functions.
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End Behaviors of Polynomial Functions

For Teachers 9th - 12th Standards
Explore the concept of graphing polynomials  with your class. Scholars graph polynomials and determine their end behavior. They use their calculator to determine the end behavior of linear, quadratic, and cubic equations.
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IB Math SL 1 - Transformations and Combinations Worksheet

For Students 10th - 12th Standards
Study transformations and combinations with your advanced math class. They solve four graphing problems by graphing the transformations of a parent graph. They determine the equations to represent the given transformations of a parent...
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Worksheet 2: Graphs, Functions and Derivatives

For Teachers 12th - Higher Ed
In this math worksheet, students answer 7 questions having to do with graphing derivatives of functions, rectilinear motion, speed and distance.
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Graphs and Transformations of Functions

For Teachers 8th - 10th
Is it possible to solve quadratic equations by factoring? It is, and your class will graph quadratic equation and functions too. They perform transformation on their graphs showing increasing and decreasing intervals, domain, and range....
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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...
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Challenge: Graphing Functions

For Students 5th - 8th
Here is a functions worksheet in which learners solve functions containing variables, graph the coordinates, and answer two questions about it. They complete 14 functions.
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Human Graph II

For Teachers 5th - 10th
Students graph the linear functions of different jobs and see how graphing linear functions always results in a straight line. In this linear functions lesson plan, students graph the jobs of gardeners and dish washers.
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Understanding the y-Intercept Student Activity Sheet 4

For Students 8th - 10th
Put it all together by exploring the y-interecept. Your algebra class solves six different problems related to defining the y-intercept on a graph. First, they identify which graph illustrate best represents the data in the table and...
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Domain and Range

For Students 7th - 9th
In this domain and range learning exercise, students write the definitions for relation, function, domain and range. They then find the domain and range of 7 sets of ordered pairs. Finally, students answer 4 questions regarding inverse...
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How Fast is the U.S. Population Growing?

For Teachers 9th - 12th
Through a mix of modeling and direct instruction, learners are introduced to exponential data. They investigate the population of the United States using the TI-nspire calculator. Multiple data representations are used to explore aspects...
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Making Connections

For Teachers 8th
Eighth graders investigate the input/output model for building function tables. From the data, 8th graders connect tables, graphs, function rules, and equations in one variable. They work backwards to determine function rules for given...
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GeoGebra Graphing Calculator

For Students 9th - Higher Ed Standards
So, exactly, what does it look like? The easily usable graphing calculator allows pupils to visualize the graph of equations and inequalities. The interactive supports any algebraic graph needed for high school mathematics and then some.
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Graph Functions with Integers

For Students 5th
Fifth graders can do a quick review of graphing functions using integers with this activity. The activity has questions which require students to identify the pertinent information in a word problem, and create a graph to represent the...
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Worksheet 6, Graphing Functions

For Teachers 9th - 10th
In this algebra worksheet students graph a given function by completing the square. They analyze a function and tell the axis of symmetry, the intercepts, and vertex. Students identify the maximum or minimum of a graph. Students identify...
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Exploration 3: Introduction to Definite Integrals

For Students 11th - 12th
In this integral worksheet, students estimate the definite integral and find the derivative of functions. They graph functions and determine the range of the velocity. This three-page worksheet contains approximately 40 problems.
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Graphing Calculator Activity: Graphing Functions

For Students 8th - 10th
In this graphing calculator worksheet, learners explore how to generate a table for a specified function and then create a graph of the function. Seven short answer and one multiple choice question is provided for individual practice.
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Getting Closer

For Students 11th - 12th Standards
Flip the script! Reverse the situation and ask the class to find the function given asymptotes. The task requires class members to use their knowledge of functions and asymptotes to create functions that have a given asymptote or...
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Exponential Graph Functions

For Students 9th - 12th
In this exponential functions worksheet, 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 each...
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Calculating And Graphing Functions

For Teachers 8th - 10th
Using a spreadsheet, computer values of functions and intervals, learners identify the domain, range and zeros of basic functions. They examine the inverse of several basic functions.
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Linear and Quadratic Functions

For Teachers 11th
In this algebra worksheet, 11th graders solve quadratic functions using the quadratic formula. They take the square roots of both side of each equation then graph both the linear and quadratic functions. There are a total of 84 problems...
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Exploring Complex Roots

For Teachers 9th - Higher Ed Standards
In exploring the concept of complex roots, students find the axis of symmetry and roots of parabolas.  Then, they discuss what makes a solution complex and how to identify functions with complex roots.
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Worksheet 4, Functions

For Teachers 8th - 9th
Eighth and ninth graders graph a given function and identify the domain, range and intercepts. Theytell the intervals that the function is increasing, decreasing, or constant. Pupils identify the minimum and maximum of the graph, and...
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How Do You Translate a Polynomial Function Vertically?

For Teachers 8th - 11th
Want to move a graphed function up or down? This is called a function translation. This video looks at translating a cubic function up three units. It considers the function in standard form, the graph of the function, and a table of...
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Techniques for Evaluating Limits

For Teachers 11th - 12th
Students read a description of how to evaluate limits then solve problems both with and without their graphing calculators. In this evaluating limits lesson, students evaluate 9 limits problems without their graphing calculators. Answers...
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Graph Functions - ELL

For Students 4th - 5th
In this ELL vocabulary acquisition worksheet, students look at the words and the pictures that show their meanings for the sea animals. Students then draw lines to connect the words with the descriptions that tell about them.
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Graph Rational Functions on a Graphing Calculator

For Teachers 9th - 11th
High schoolers graph functions on their graphing calculators. They follow step-by-step directions to enter rational functions onto their calculators and then graph them. The worksheet includes nine questions.
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EngageNY

Revisiting the Graphs of the Trigonometric Functions

For Teachers 11th - 12th Standards
Use the graphs of the trigonometric functions to set the stage to inverse functions. The lesson reviews the graphs of the basic trigonometric functions and their transformations. Pupils use their knowledge of graphing functions to model...
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Party Graphs: Enrichment

For Students 6th - 7th
In this graphing worksheet, learners match each graph with the items for the party. Students then label the graphs and write the function each graph shows.
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Functions

For Students 9th - 12th
In this functions worksheet, students graph 2 functions involving exponents and quadratics . Students then evaluate 3 quadratic functions given values.
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Chapter 3, Worksheet 3Z: Pre-Calculus

For Students 9th - Higher Ed
In this pre-calculus learning exercise, students graph 18 equations on a calculator. Then they create a sketch of each the graph as it appears on the calculator.
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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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SAT Prep: Test 4 Section 2 Part 5

For Students 9th - 12th
Picking up where he left off (problem 17), Sal demonstrates graphing functions with an informative and clear explanation. Additionally, problem 18 involves finding the values of angles in an equilateral triangle.
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Problem-Solving Applications: Use Functions and Graphs

For Students 4th - 8th
Upper elementary and middle schoolers examine a graph that compares water temperature during 10 minutes of heating. They use the information from the graph to solve two word problems and then write an explanation of how they solved the...
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Calculus Grapher

For Teachers 8th - 12th Standards
Learners draw a graph of any function to see its derivative and integral in this simple, yet informative, simulation. Other options include manipulating the scale, the shape of the graph, and the angle. 
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Graphing Functions #1

For Students 7th - 8th
For this graphing linear functions worksheet, students evaluate six linear functions for ordered pairs. They graph the results on a coordinate grid.
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Draw the Inverse for Ten Graphed Functions

For Students 11th - Higher Ed
In this inverse function activity, students draw the inverse function for ten given graphs.  Inverses may not exist for all functions.
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Graphing Functions With 2 Points and From a Graph

For Teachers 9th - 11th
Students plot points on a coordinate plane. They describe, in words, methods for finding the slope of a line. After given a worksheet, students read instructions, draw a Cartesian plane, plot ordered pairs, and graph lines. Papers are...
1 In 1 Collection
EngageNY

Graphs of Functions and Equations

For Teachers 8th Standards
Explore the graphs of functions and equations with a resource that teaches scholars how to graph functions as a set of input-output points. They learn how the graph of a function is the graph of its associated equation.
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All In The Family

For Teachers 10th - 12th
Compare function families and determine the similarities and differences of the square root, exponential and logistic families. Have them graph function families and compare the equations, graphs, and the domain and range of each. One...
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Introduction to Curve Sketching

For Students 10th - 12th Standards
Practice makes perfect! Give young mathematicians practice graphing functions and their inverses. Discussion questions are provided to help learners think about the relationship between functions and their derivatives.
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Graph Square Root and Cube Root Functions

For Teachers 9th - 11th
Scholars first learn to graph square root and cube root functions by creating a table of values. They then learn how to graph functions from transformation of the graphs of the parent square root and cube root functions.
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Module 4: Rational Functions

For Students 9th - 12th Standards
Time to study the most sensible function — rational functions! The seven-lesson unit develops the concept of a rational function through a connection to rational numbers and fractions. Scholars graph functions, solve equations, and...
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Worksheet 9: Trig Functions

For Teachers 12th - Higher Ed
For this math worksheet, students are given 7 problems in which they write expressions for trig functions, compute limits and graph functions.
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Exit Ticket: Graphs of Functions

For Students 9th - 11th Standards
This learning exercise 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,...
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All-in-All Problems

For Students 9th - 11th Standards
Graphs, functions, symbols, and more! Use these strategies to model everything from the flow of a river to the number of cars passing a toll booth. Presented differently but solved similarly, learners consider five different scenarios...
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Getting Started Dilemma

For Teachers 8th - 10th Standards
Get out those thinking caps and apply graphing functions to a real-world problem. Use the TI-83 graphing calculator to evaluate algebraic expressions that are imbedded in a series of real-world scenarios. A great lesson!
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Derivate

For Students 11th - Higher Ed
Derive tangent lines through derivatives. Scholars use an app to graph functions and investigate derivatives and tangent lines. The interactive automatically graphs a tangent line at a specified point and can also produce tables of values.
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Open Sets, Limits, Continuity

For Students Higher Ed
In this open sets worksheet, students give characteristics of an open set under given conditions. They graph functions and define limits. This two-page worksheet contains 3 multi-step problems with explanations.
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Tangent Lines

For Teachers 10th - 12th Standards
Making the leap from graphing functions to talking about the slope of curves is eased into with the help of worksheets and presentations like this one. With an emphasis on connections to limits and velocities, without ever saying the...
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Too Big, or Not Too Big

For Students 9th - 12th Standards
Determine whether the point is just right. The interactive allows participants to input a constraint equation. Pupils pick a point and determine whether it is too big, not too big, or just right for the constraint. Using the graphing...
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Writing and Graphing Functions

For Teachers 7th - 9th
Students explore mathematics by completing a graphing assignment in class. In this math functions lesson, students practice graphing X and Y coordinates on a graph and checking their work with partners. Students complete more graphing...
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Algebra: Graph Functions

For Students 6th
For this algebra worksheet, student review the steps for drawing a graph to represent the function y=x+4. They complete a table of function for each of 3 given functions and use graph paper to graph each function.
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Graphical Consequences of Continuity

For Teachers 8th - 12th
Learners explore and examine the continuity of three functions: horizontal zooming, polynomial function, and oscillating functions. They practice graphing functions, generating tables and navigating the zoom, vars and test menus on their...
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Test on Functions

For Students 8th - 10th
Upper graders identify the domain, range, maximum and minimum value of graphs. They graph functions and plot ordered pairs, then solve functions with given domains. This two-page activity contains 25 problems.
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Worksheet 13 - Derivative

For Teachers Higher Ed
In this derivative of a power worksheet, students compare derivatives of functions, and graph functions. This one-page worksheet contains five multi-step problems.
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Worksheet Analysis Section 2.2: Function

For Students 10th - 12th
In this function worksheet, students identify a given function as odd, even, or neither. They graph functions on a coordinate plane. This two-page worksheet contains 13 multi-step problems.
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Algebra 1-2 Fall Final Exam Open-Ended Review

For Students 9th - 11th
Have a final exam coming up? This 7 page packet contains 50 problems for your Algebra 1-2 class to complete as test prep or practice. They write algebraic equations, graph functions, identify the domain and range, determine the slope,...
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Worksheet 3 - Velocity, Movement

For Teachers Higher Ed
In this velocity worksheet, students determine the distance traveled when an object is moving in a straight line. Students graph functions and determine the slope of the line. This two-page worksheet contains six multi-step problems.
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MTEL Math Practice Test: 36-40

For Students 11th - Higher Ed
Sal goes into detail in solving these problems on the practice MTEL math test, especially with the complicated details of question 36. Viewers will rest assured in the easy confidence with which Sal addresses these increasingly difficult...
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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

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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Graphs (2004)

For Teachers 9th - 12th Standards
Show your pupils that perimeter is linear and area is quadratic in nature with a short assessment task that requests learners to connect the graph and equation to a description about perimeter or area. Scholars then provide a...
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Transformational Graphing

For Students 9th - 12th Standards
Find relationships between the structure of a function and its graph. An engaging lesson explores seven parent functions and their graphs. Learners match functions to their graphs and describe transformations.
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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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F.IF.C.7.b Assessment Items

For Teachers 9th - 12th Standards
Here's a special resource for some special functions. Young mathematicians show their understanding of square root, cube root, absolute value, and piecewise functions through a set of assessment items. They graph these functions and, in...
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Graphs of Linear Functions

For Students 8th Standards
What does a slope of 2/3 mean? Develop an understanding of the key features of a linear function. Pupils graph the linear functions and explain the meaning of the slope and intercepts of the graphs. 
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Tables of Linear Functions

For Students 8th Standards
Don't forget the tables! The previous lessons in this five-part series examined the linear equation and graph relationship. The current lesson adds tables to the mix. At completion, individuals should be able to create a table of values,...
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Explorations 5: Introduction to Limits

For Students 10th - 12th
In this limit activity, students find the interval values of given functions. They identify constants, and plot graphs. This three-page activity contains approximately 20 problems.
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The Box Problem

For Teachers 9th - 12th
High schoolers explore the concept of volume.  In this volume lesson, students use their Ti-Nspire to maximize the volume of a box.  High schoolers determine the dimensions that will yield the greatest volume.  Students graph the volume...
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Graphs of Functions

For Students 9th
In this graphs of functions worksheet, 9th graders solve and complete 3 different types of problems. First, they graph function f given by the functions shown on the grid. Then, students find the inverse of a function including its...
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Functions and the Vertical Line Test

For Teachers 7th - 9th
Students examine functions and function notation. They use computer activities to discover how to graph functions, and conduct a vertical line test. Students describe spatial relationships using coordinate geometry.
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Chapter 7. Functions and Graphs

For Students 9th - 11th
In this functions and graphs worksheet, students determine the domain and range of a given relation.  They graph functions on a coordinate plane and write equations in the slope-intercept form.  This twelve page worksheet contains 30...
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Exercise Set 1.5: Inverse Functions

For Teachers 11th - Higher Ed
In this inverse functions worksheet, young scholars review inverse functions. They solve 66 questions. Problems cover a wide variety of types. Students graph functions and their inverses, they identify one-to-one functions and the...
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7 Lesson Plan: Inverse Functions

For Teachers 10th - 12th
Students evaluate inverse functions.  In this inverse function lesson, students identify the domain and range of inverse functions.  They use their graphing calculator to graph functions.  Students justify their work through open-ended...
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Reflections of Basic Functions

For Students 10th - 12th
In this reflections of basic functions learning exercise, students graph functions.  They identify transformations, dilations and reflections.  Students lable the vertices and intercepts.  This two-page learning exercise contains 10...
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Natural Logarithm

For Teachers 9th - 12th Standards
Young mathematicians solve problems of logs and natural logs. They graph functions of natural logs on the TI and relate integrals to natural logarithms.
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One to One Functions

For Students 9th - 12th
In this one to one functions learning exercise, students solve 27 short answer and graphing problems.  Students determine if a function is one to one given a graph or an equation.  Students graph functions to determine if it is one to one.
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Variables, Formulas, Functions, Graphs

For Students 12th - Higher Ed
In this function learning exercise, students are given 6 short-answer problems regarding formulas vs. functions, graphing functions and different ways to view functions.
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Epsilon-Delta Window Challenge

For Teachers 9th - 12th Standards
Students graph functions and analyze them. In this calculus lesson, students define limit formally using Epsilon-Delta. They use the TI to graph the function and analyze it.
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Functions and Limits

For Students 12th - Higher Ed
In this functions and limits instructional activity, students find the discontinuities of a function and classify them as removable or non-removable. They identify the limits of a function. Students graph functions. This four-page...
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Algebra 1 Unit 5 Review

For Students 6th - 7th
In this problem solving worksheet, students simplify 2 math expressions, evaluate 1 expression and convert to fractions as instructed. Students find the first 3 terms of one equation, complete 2 graph functions and answer 1 word problem.
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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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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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Chart of Parent Functions

For Students 9th - 11th Standards
The characteristics of parent function vary from graph to graph. Let learners decipher the graph, table of values, equations, and any characteristics of those function families to use as a guide. The nicely organized page displays the...
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The Fall of Javert

For Teachers 9th - 12th Standards
Falling off a bridge might not sound like your idea of a good math problem, but incorporating the final scene of Les Misérables is sure to spark interest. The goal is to use the time Javert fell off the bridge to determine how high he...
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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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Domain and Range 2

For Students 6th - 9th
The short example shown in this video starts with a given a set of numbers in the domain and the range that represent a function. One needs to simply map the points on a coordinate plane.
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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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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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California State Standards: Algebra I

For Students 8th - 10th Standards
Starting a year of Algebra I? This mighty packet practices all of the major topics with different ranges of difficulty. Standards include everything from linear to quadratic to rational expressions. Use it in a variety of ways to...
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Impossible Graphs

For Teachers 6th - 8th
Middle schoolers practice plotting functions on the Cartesian coordinate plane while participating in a discussion about the Possible Or Not worksheet/activity. Students also use the Impossible Graphs worksheet to practice reading a...
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Linear Functions: Slope, Graphs, and Models

For Teachers 8th - 9th
This math packet provides an opportunity for learners to graph two linear equations on a coordinate grid and determine the slope and y-intercept of each. They use the equation of five lines to find the slope and y-intercepts, and then...
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How Do You Find the Y-Coordinate of a Point on a Line If You Have a Graph?

For Teachers 7th - 9th
Looking at the graph of a given linear equation, find the y(4). What? What does that even mean, find y(4)? Watch this video and the teacher will show and tell everything about finding the y(4) from the given graph.
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Understanding the y-Intercept Activity Sheet 2

For Students 8th - 10th
Understand the y-intercept by solving 13 various types of problems. They involve defining the y-intercept's representation in the graph and why it is negative. Then, they determine which function rule relates to the graph. They also...
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Graphing Linear Equations Cards

For Students 8th - 9th Standards
OK, so maybe graphing linear equations can be fun. This activity includes a set of linear equation cards to be cut and place face up on a table. Learners pick a card and match it to the correct graph card. This is a really fun way to...
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Rate of Change 1

For Teachers 10th - 11th
In this rate of change worksheet, students use functions to determine the velocity of an object. This two-page worksheet contains ten problems.
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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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Graph Logarithmic Functions

For Students 11th - 12th
Practice graphing with this learning exercise. High schoolers solve logarithms and graph the solution. This one-page learning exercise contains eight problems, varying in complexity.
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Rate of Change in a Linear Relationship

For Students 8th - 10th
Check out linear equations with this worksheet. Pupils observe and analyze linear equations and identify the rate of change in linear functions. There are 10 questions on two pages.
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Using Parallel Axes To Discover Mathematical Interconnections

For Teachers 6th - 8th
In this math worksheet, students graph the functions on parallel axes and observe the location of the slope point in relation to the x and y axes.
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How Do You Determine if an Ordered Pair is a Solution to an Equation?

For Teachers 7th - 9th
There are several ways to determine if an ordered pair is the solution to a linear equation. The ordered pair can be plugged in to the equation to check if it's a solution. However, in this video the instructor sets up a table and plugs...
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2D Graphing Functions

For Students 9th - 10th
In this algebra activity, students use a table to graph their x and y values by plugging it into the equation and solving. They plot their points and analyze their data. There are 6 graphing questions.
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Module 7: Modeling with Functions

For Students 9th - 12th Standards
The sky's the limit of what you create when combining functions! The module begins with a review of transformations of parent functions and then moves to combining different function types using addition, subtraction, and multiplication....
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Graphing Piecewise Functions

For Teachers 8th - 10th Standards
Step up to learn about step functions. The lesson, designed for high schoolers, first covers piecewise functions and how to draw their graphs. It then introduces step functions, including the greatest integer (floor) and ceiling functions.
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Transformations of the Graphs of Logarithmic and Exponential Functions

For Teachers 10th - 12th Standards
Transform your activity 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...
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Increasing and Decreasing Functions 1

For Teachers 8th Standards
Model situations with graphs. In the fourth installment of a 16-part module, scholars learn to qualitatively analyze graphs of piecewise linear functions in context. They learn to sketch graphs for different situations.
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Graphing the Logarithmic Function

For Teachers 10th - 12th Standards
Teach collaboration and communication skills in addition to graphing logarithmic functions. Scholars in different groups graph different logarithmic functions by hand using provided coordinate points. These graphs provide the basis for...
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Graphs of Simple Nonlinear Functions

For Teachers 8th Standards
Time to move on to nonlinear functions. Scholars create input/output tables and use these to graph simple nonlinear functions. They calculate rates of change to distinguish between linear and nonlinear functions.
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Saxon Math: Algebra 2 (Section 11)

For Teachers 9th - 12th Standards
As we approach the end of the Saxon math sections, the 11th of 12 units begins the process of summarizing and combining material from the previous lessons. The relationships between functions and their transformations are investigated,...
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Graphing Family of Functions

For Teachers 8th - 10th
Functions have families, too. Learners first graph the parent functions for linear, quadratic, and cubic functions, and then use vertical translations to graph families of functions.
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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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Review Unit 3: Functions

For Students 8th Standards
Time to show what you know about functions! The review concludes a series of nine lessons on the basics of functions. The problems included are modeled from the previous lessons. Pupils determine if a table represents a function,...
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The Graph of the Natural Logarithm Function

For Teachers 10th - 12th Standards
If two is company and three's a crowd, then what's e? Scholars observe how changes in the base affect the graph of a logarithmic function. They then graph the natural logarithm function and learn that all logarithmic functions can be...
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Identifying Quadratic Functions (Vertex Form)

For Students 9th - 12th Standards
Pupils calculate the equation of a quadratic in vertex form from a specific graph and determine an equation that would fit the description of a parabola. The final question determines the individuals' understanding of the signs of the...
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Derivative Grapher

For Teachers 11th - 12th
Follow the slope in real time. Using graphs created with Desmos, pupils compare the graph of a function to the graph of its derivative. Pairs then work together to create derivative graphs of their own.
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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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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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Using Motion Sensors to Explore Graph Sketching

For Teachers 11th - Higher Ed
Get moving to a better understanding of graphs of derivatives. Using motion sensors, scholars vary their velocities to create graphs of the first derivative of a function. The activity challenges groups to first create a script of the...
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Graphing Quadratics

For Students 8th - 12th Standards
Quadratics only have three terms, but each one is fairly important. Scholars use an interactive to explore how each coefficient affects the graph of a quadratic function. They also see how changes to the vertex form and how changes to...
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Quadratic Reflections

For Students 9th - 12th Standards
Reflect upon the graphs of quadratic functions. Given a quadratic function to graph, pupils determine whether the graph after a horizontal and vertical reflection is still a function. The final two questions ask scholars to describe a...
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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...
1 In 1 Collection 5:12
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Function Families and Their Connections Including Vertical Shift of an Absolute Value Function

For Teachers 9th - 12th Standards
One of the strongest tools an algebra learner develops is the ability to quickly and accurately graph almost any given function. Often doing this quickly and accurately requires rigid transformations to a parent function, demonstrated in...
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Comparing Functions—Linear

For Students 9th - 12th Standards
Identify transformations of linear functions. Given the graph of the linear parent function, pupils compare the graphs of four other linear functions and determine how the graphs of each linear function relates to the graph of y = x.
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Desmos Graphing Calculator

For Students 9th - Higher Ed Standards
They say a graph is worth a thousand points. The interactive allows users to graph a wide variety of functions and equations. Using the included keyboard or typing directly into the list, learners determine the graph of a function....
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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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Key Features of Graphs

For Teachers 9th - 11th Standards
The key is ... After a day of instruction on key features of graphs, groups create a poster and presentation on the key features of their given function graph. The resource provides an extension activity of "telephone" using graphs.
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As the Wheel Turns

For Students 9th - 12th Standards
Determine the location of a point on a moving wheel. The task challenges groups to determine the horizontal and vertical locations of a point on the edge of wheel that is moving. Teams first determine a function that will model the...
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Exploring Sinusoidal Functions

For Students 9th - 12th Standards
What effect does changing a parameter have on the graph of a trigonometric function? Pupils use a Desmos applet to explore the general sine graph. They experiment changing different parameters and record the resulting change of the...
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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...
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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...
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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...
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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...
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Dilations of Quadratic Graphs - Concept

For Students 8th - 10th Standards
Help learners recognize the characteristics of a quadratic graph and how changes affect them. An informative video uses a graphing calculator in order to find out what happens when the leading coefficient of a quadratic changes. The...
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Parabola Project

For Teachers 9th - 12th Standards
Class members select a picture that contains a parabola and construct a drawing of it using function graphs in the quadratic project. Individuals restrict the domains of the functions to create a more accurate drawing. They then submit a...
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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.
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Symbolic Similarity

For Students 9th - 11th Standards
How many things does one transformation tell you? Learners compare and contrast the graphs of different parent functions with the same transformation. Using a rational and absolute value function, pupils identify key features of their...
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People and Places

For Students 7th - 12th Standards
Graph growth in the US. Given population and area data for the United States for a period of 200 years, class members create graphs to interpret the growth over time. Graphs include population, area, population density, and population...
1 In 1 Collection 11:40
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Function Families: Translations and Reflections

For Teachers 9th - 12th Standards
This comprehensive introduction to rigid transformation of functions does a fabulous job of breaking down translations and reflections into manageable concept chunks. Care is taken with horizontal translations, vertical translations,...
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Pre-Test Unit 3: Functions

For Students 8th Standards
How does an input affect an output? Assess your learners' ability to answer this question using this pre-test. Scholars answer questions about the basics of a function. Topics include determining if a table or statement represents a...
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Write the Equations

For Students 9th - 12th Standards
What is the equation of the new absolute value function when it is moved? The assessment provides a graph of the parent absolute value function. Given three other graphs of a single transformation of a function, pupils determine the...
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Multi-Function Data Flyer

For Students 8th - 12th Standards
Explore different types of functions using an interactive lesson. Learners enter functions and view the accompanying graphs. They can choose to show key features or adjust the scale of the graph.
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Functions by the Slice

For Students 11th - 12th Standards
Piece by piece ... dismantling a function can highlight interesting patterns. The task asks learners to slice functions in sections with the same vertical change. They then recreate the graph with these slices positioned horizontally....
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Rising Prices

For Students 9th - 12th Standards
What will that cost in the future? The scenario provides pupils with a growth as a Consumer Price Index. Learners create functions for a given item to determine future prices and graph them. Class members then compare their functions to...