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Interactive
CK-12 Foundation

Infinite Limit Type: Evaluating Limits of Rational Functions

For Students 11th - Higher Ed Standards
Rational functions become less mysterious when you know about limits. Individuals use an interactive to move a rational function on a coordinate plane and to investigate function values for certain x-values. They see how the limit...
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Lesson Plan
Curated OER

Graphing Rational Functions

For Teachers 9th - Higher Ed Standards
Learners complete an activity, included, of the information on asymptotes and intercepts. They also solve and complete eight questions on graphing rational functions, file included. Finally, pupils summarize vertical asymptotes,...
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Worksheet
Curated OER

Rational Functions

For Students 9th - 11th
In this rational functions worksheet, students identify rational functions.  They find the domain and range of each function.  Students find the x and y-intercepts of functions.  This two-page worksheet contains 35 multip-step problems.
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Lesson Plan
Curated OER

Asymptotes and Zeros

For Teachers 9th - 12th Standards
Learn how to explore rational functions and investigate the graphs rational functions and identify its singularities and asymptotes.  Young scholars approximate the solutions to rational equations and inequalities by graphing.
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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

Math Regents Exam Questions: Graphing Rational Functions

For Students 9th - 12th
In this graphing rational functions activity, 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.
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Lesson Plan
Curated OER

Asymptotes And Zeros of Rational Functions

For Teachers 9th - 12th Standards
Budding mathematicians graph polynomial functions and examine their zero and y-intercepts. They analyze how the zero and y-intercepts of the numerator and denominator affect the graph of a rational function. Several great additional...
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Worksheet
Curated OER

Graphing Rational Functions

For Students 11th
In this Algebra II worksheet, 11th graders graph rational functions and use the graph to solve real-life problems. The four page worksheet contains forty-one problems. Answers are not provided.
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Worksheet
Curated OER

Rational Functions and Their Graphs

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

A Slant Asymptote

For Teachers 9th - 12th
In this slant asymptote worksheet, students solve 1 rational equation.  Students determine the slant asymptote of a rational equation.
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Worksheet
Curated OER

Horizontal Asymptotes: M=N, M>N

For Students 9th - 12th
In this algebra worksheet, students calculate the horizontal asymptote for rational functions, whose leading exponents follow the rules: M = N or M > N. There are 4 questions.
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Lesson Plan
Curated OER

Exploring Vertical Asymptotes

For Teachers 9th - 12th Standards
Scholars identify the domain of a rational function in this precalculus lesson. They identify the removable discontinuity and label what will make the denominator zero. Learners also describe properties of the graph as it relates to the...
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Assessment
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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

Crossing the Asymptote

For Teachers 9th - 11th
Students investigate graphs and their asymptotes. In this precalculus lesson, students examine the numerator and denominator of their rational functions. This helps them identify where and when the graph will cross its asymptote.
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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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Lesson Plan
Curated OER

Worksheet 9, Rational Functions

For Teachers 9th - 10th
In this algebra worksheet, students tell how they would find the domain of a rational function. They find the intercepts of a rational function and graph it. Students test for symmetry, locate the asymptotes and determine where the graph...
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Lesson Plan
Curated OER

Rational Functions

For Teachers 10th - 12th
In this algebra worksheet, students solve rational functions and identify the x and y intercepts, the vertical and horizontal asymptotes. There are 26 questions.
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Worksheet
Curated OER

Rational Expressions Test with a Calculator

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

Math Worksheet: Graphs of Rations Functions (2)

For Students 11th
In this Algebra II worksheet, 11th graders examine a rational function as they determine the domain, vertical asymptotes, x- and y-intercepts and graph the function.  The two page worksheet contains five problems that relate to the one...
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Lesson Plan
Curated OER

Rational Functions

For Teachers 9th - 11th
Young scholars evaluate rational functions. In this precalculus lesson, students make observations and define what makes a rational function and what makes a linear function. They use the Ti calculator to visualize the different graphs.
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Worksheet
Curated OER

Rational Functions

For Students 11th - 12th
In this Algebra II/Pre-calculus learning exercise, students solve and graph rational equations, identifying the intercepts and asymptotes. The six page learning exercise contains nine problems. Answers are not provided.
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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.