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Worksheet
Curated OER

Vertical Asymptotes: M=N and M=N+1

For Students 9th - 12th
In this algebra activity, students determine the vertical asymptotes for a given rational equation with the leading exponents following either of the cases: M = N or M = N + 1. There are 4 questions.
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Lesson Plan
Curated OER

Worksheet 7 - Asymptote

For Teachers Higher Ed
For this asymptote worksheet, students compute limits, graph vertical asymptotes, and find the slope of the secant line. This one-page worksheet contains six multi-step worksheets.
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Assessment
1
1
Balanced Assessment

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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Lesson Plan
Curated OER

Worksheet 4 - function

For Teachers Higher Ed
In this function worksheet, students identify functions, express decimals as fractions and write decimals as a geometric series. This one-page worksheet contains six multi-step problems.
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Worksheet
Curated OER

Graph, Identify Asymptotes, Find Domain and Range, for Eleven Simple Rational Functions

For Students 10th - 12th
Using this worksheet, pupils graph 11 simple rational functions. They also find asymptotes, domain, and range for each function. The solutions are provided.
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Worksheet
Curated OER

Infinite Limits and Horizontal Asymptotes

For Students Higher Ed
In this infinite limit worksheet, students compute horizontal and vertical asymptotes. They use trigonometric functions to find the limits of functions and compare results. This two-page worksheet contains examples and explanations and...
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Worksheet
Curated OER

Graphing a Rational Function

For Students 10th - 12th
In this graphing rational functions worksheet, students find the domain, asymptotes, intercepts and graph a given rational function.  A grid for the graph is provided.
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Worksheet
Curated OER

Rational Expressions/Equations Test

For Students 10th - 12th
In this Algebra II worksheet, students are given a test of twenty-three problems regarding Rational Expressions and Rational Equations.  Some of the questions are multiple choice, while others are word problems or problem solving problems.
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Worksheet
Curated OER

Lesson 19: Rational Functions and Long Division

For Students 10th - 12th
Explore rational functions with this packet. A lot of information is provided, including several examples. Learners graph rational functions and find vertical, horizontal, and oblique asymptotes. This seven-page worksheet contains...
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Worksheet
Curated OER

Graphing Rational Functions

For Students 9th - 10th
In this rational function worksheet, students identify the vertical and horizontal asymptote for each rational function. They graph rational functions. This one-page worksheet contains five problems.
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Assessment
Concord Consortium

Rational and Not So Rational Functions

For Students 11th - 12th Standards
Do not cross the line while graphing. Provided with several coordinate axes along with asymptotes, pupils determine two functions that will fit the given restrictions. Scholars then determine other geometrical relationships of asymptotes...
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AP Test Prep
1
1
Flipped Math

Calculus AB/BC End of Unit 1 Review: Limits and Continuity

For Students 10th - 12th
Test the limits of one's knowledge on continuity. The last of 18 installments in Unit 1 - Limits and Continuity is an end-of-unit review learning exercise. Individuals identify and classify discontinuities, investigate continuity at a...
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Worksheet
Curated OER

Discussion Sheet 6: Doman & Range

For Students Higher Ed
In this domain and range worksheet, students determine the domain, range, x and y-intercepts, vertical, horizontal and asymptotes for a function. They write a formula for a function for given properties. Students read story problems...
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Lesson Plan
Curated OER

Worksheet 28 - Functions

For Teachers Higher Ed
For this function worksheet, students identify functions which are their own derivative. They determine the vertical and horizontal asymptotes of functions. This one-page worksheet contains seven multi-step problems.
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Worksheet
1
1
Curated OER

Rational Functions

For Students Higher Ed
In this college level Pre-Calculus activity students evaluate rational functions, identify the domain, vertical asymptotes, and x- and y-intercepts.  The three page activity contains forty problems.  Answers are provided. 
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Worksheet
Curated OER

Graphing Functions

For Students 11th - Higher Ed
In this graphing functions worksheet, students 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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Worksheet
Curated OER

Simplifying Functions

For Students 11th
In this simplifying functions worksheet, 11th graders solve and complete 11 different types of problems. First, they simplify each function as necessary. Then, students state the vertical asymptotes, holes, horizontal asymptotes, domain...
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Worksheet
Mt. San Antonio Collage

Graphs of Rational Functions

For Students 9th - 12th Standards
Sometimes graphing rational functions can feel a little "irrational." Starting with the basics, learners work their way through the pieces of these graphs and finish off with an application question. 
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Worksheet
Curated OER

Limits at Infinity and Horizontal Asymptotes

For Students Higher Ed
In this limits worksheet, students sketch the graph of a function. They complete three fill in the blank questions. Students solve fifteen limits problems. They use L'Hopital's Rule to solve four problems. Students find the vertical...
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Worksheet
Curated OER

Graphs of Functions

For Students 10th - 12th
In this graphs of functions worksheet, students identify the domain and range of a function. They determine the vertical horizontal asymptote and find the y and x intercepts. Students sketch a graph of the function. This one-page...
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Worksheet
Curated OER

Rational Functions and Their Graphs

For Students 11th
In this Algebra II worksheet, 11th graders examine the graphs of rational functions, identifying the points of discontinuity and the vertical and horizontal asymptotes.  The three page worksheet contains explanation of topic, several...
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Worksheet
Curated OER

Rational Expressions Test with a Calculator

For Students 11th - Higher Ed
In this rational expression activity, students graph rational equations, evaluate limits, state intercepts, asymptotes, and roots and factor.  This activity is designed as a test to be completed with a calculator. 
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Worksheet
Curated OER

Twenty Rational Function Problems

For Students 10th - 12th
In this rational functions learning exercise, students find asymptotes, perform operations, simplify, and solve in twenty rational functions.
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Worksheet
Curated OER

Algebra II Chapter 11 Test

For Students 10th - 11th
In this Algebra II worksheet, students assess their knowledge of rational algebraic expressions. The three page worksheet contains a combination of twenty-three multiple choice, short answer, and word problems. Answers are not provided.