EngageNY
Rational Functions
Make a connection between rational expressions and rational functions. Pupils review simplifying and performing operations on rational expressions and recall what it means for two rational expressions to be equivalent based on their...
EngageNY
Graphing Rational Functions
Put everything together in a picture. Scholars take what they learned in the previous three lessons in the 15th segment of a 23-part unit to graph rational functions. They find the end behavior, the horizontal and vertical asymptotes if...
EngageNY
Transforming Rational Functions
Move all rational functions—well, maybe. Learners investigate the graphs of the reciprocals of power functions to determine a pattern between the graph and the power. Pupils graph rational functions where transformations are clearly...
EngageNY
Horizontal and Vertical Asymptotes of Graphs of Rational Functions
Get close to your favorite line. Scholars use end behavior to help find horizontal asymptotes. With the understanding of domains of rational functions, learners find vertical asymptotes and then use graphing calculators to verify the...
EngageNY
End Behavior of Rational Functions
Connect end behavior to previous learning. Pupils connect finding the end behavior of rational functions to finding end behavior of polynomial functions. The 13th segment in a 23-part unit starts with finding the end behavior or power...
Mt. San Antonio Collage
Test 2: Rationals, Exponentials, and Logarithms
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.
Radford University
Function Family Fun
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...
Mt. San Antonio Collage
Quiz 2: Types of Functions
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.
Mathematics Assessment Project
Representing Functions of Everyday Situations
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.
Shmoop
Functions Worksheet 6
Instead of the typical function application problems, learners think a little deeper through these ten problems. Multiple types of functions are represented and the questions add a variety of thinking to practice their skills.
Mt. San Antonio Collage
Test 1: Graphing Functions
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.
Education Development Center
Creating a Polynomial Function to Fit a Table
Discover relationships between linear and nonlinear functions. Initially, a set of data seems linear, but upon further exploration, pupils realize the data can model an infinite number of functions. Scholars use multiple representations...
Curated OER
Do Two Points Always Determine a Linear Function II?
Learners analyze the difference between the slope intercept and standard forms of a line in this task. Given two general points using letters they explore linear functions and linear equations.
Mt. San Antonio Collage
Quiz 1: Functions, Domain and Range
Take the work out of worksheets and use these problems and worked-out answer key as a resource. The problems reinforce skills in domain and range, identifying graphs, and even and odd functions.
Illustrative Mathematics
Chicken and Steak, Variation 2
Many organizations put on barbecues in order to make money. In a real-world math problem, the money allotted to purchase steak and chicken at this barbecue is only one hundred dollars. It is up to your potential chefs to figure out how...
EngageNY
Wishful Thinking—Does Linearity Hold? (Part 2)
Trying to find a linear transformation is like finding a needle in a haystack. The second lesson in the series of 32 continues to explore the concept of linearity started in the first lesson. The class explores trigonometric, rational,...
Virginia Department of Education
Curve of Best Fit
Which function models the data best? Pupils work through several activities to model data with a variety of functions. Individuals begin by reviewing the shapes of the functions and finding functions that will fit plotted data points. By...
Curated OER
Rumors
Your young gossipers write an exponential function for the number of people who have heard a rumor after a number of days have passed. Learners then answer a series of questions, including whether or not the solutions are realistic by...
Curated OER
Skeleton Tower
Your algebra learners build a quadratic function in this task of counting the blocks used to build objects. The arithmetic sequence that shows up brings up a shortcut to the long addition using the Gauss Method. Eventually, learners...
EngageNY
Wishful Thinking—Does Linearity Hold? (Part 1)
Not all linear functions are linear transformations — show your class the difference. The first lesson in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...
Curated OER
The Canoe Trip, Variation 2
The behavior of a rational function near a vertical asymptote is the focus around this trip up a river. Specifically, numerical and graphical understanding is studied. The canoe context pushes the variables as numbers, rather than as...
EngageNY
Modeling with Quadratic Functions (part 2)
How many points are needed to define a unique parabola? Individuals work with data to answer this question. Ultimately, they determine the quadratic model when given three points. The concept is applied to data from a dropped...
West Contra Costa Unified School District
Derivative – Standard Definition
Making a clear connection to algebra concepts helps learners understand the definition of a derivative. The lesson plan begins with looking at limits of simple linear and rational functions, and leads to the definition of...
Curated OER
Summer Intern
Your young apprentices build a function describing the percent concentration of salt in a brine. The rational function is then related to the parent function, y= 1/x, and graphed. Finally, the apprentices predict the amount of fresh...
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