Texas Instruments
Graphs of Rational Functions
Take your kids on a tour of graphing rational functions. Using this TI lesson, high schoolers identify the end behavior of their functions. They find the domain and range, describe end behavior, and look at asymptotes and restrictions of...
Curated OER
Worksheet 7 - Asymptote
In 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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Senior Analysis: Graphing Rational Functions
Budding mathematicians graph given functions, identify the asymptotes, graph absolute values, and write a table of points. This three-page worksheet contains 23 problems.
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Lesson 19: Rational Functions and Long Division
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 activity contains...
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Writing Equations of Hyperbolas
In this writing equations activity, students write the equations of a hyperbola. This four-page activity contains 24 problems. Answers are provided on the last two pages.
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Graphs of Functions
For 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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Graphing Functions
In this graphing functions activity, 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 draw and...
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Evaluating Limits
In this evaluating limits worksheet, students solve and complete 20 various types of problems. First, they determine the highest power of x in the function. Then, students divide both the numerator and the denominator by that power....
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Evaluating Limits
In this evaluating limits worksheet, students solve and complete 14 different types of problem. First, they determine the highest power of x in the function. Then, students divide both the numerator and the denominator by that power....
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Evaluating Limits
In this evaluating limits worksheet, students solve and complete 22 various types of problems. First, they determine the highest power of x in each of the functions. Then, students divide both the numerator and the denominator by that...
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Graphing Functions
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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Hyperbolas
In this hyperbolas worksheet, 11th graders solve and complete 5 different problems. First, they define hyperbolas and draw a picture of one. Then, students find the coordinates of the vertices and the foci and the equation for the...
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Intuitive Approach to Limits
Students identify and comprehend the concept of limit in mathematics. They also view artistic works illustrating limits by M. C. Escher and apply techniques of one-sided limits to graphs of relations. Finally, students compute limits...
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Graphing Review
in this graphing review instructional activity, students solve a variety of problems such as interpreting parabolas, identifying intercepts and asymptotes, and identifying functions. They solve piecewise functions and rational functions....
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Inflection Points
In this inflection points learning exercise, 11th graders solve and complete 5 different problems. First, they find intervals of x for which each of the following curves is increasing, decreasing, concave upward, concave downward. Then,...
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Chapter 3: Practice Test - Functions
For this function worksheet, students find the inverse of functions, determine the horizontal asymptote of functions and graph functions. This three-page worksheet contains 27 problems.
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Hyperbolas
Students locate and identify the center, foci, vertices, and asymptotes fo hyperbolas. They graph equations involving asymptotes and hyperbolas. Finally, students determine the equation of a hyperbola with a horizontal transverse axis.
Purple Math
Purplemath: Conics: Hyperbolas
A three-part tutorial that discusses the basic terms, definitions, and formulas related to hyperbolas.
Cuemath
Cuemath: Rational Function
A comprehensive guide for learning all about rational functions with definitions, how to plot them, solved examples, and practice questions.
Curated OER
Zona Land
Site explains asymptotes well using reciprocal function as example. Points out weaknesses that technology has when graphs are close to asymptotes.
Mathematics Archives
Math Archives: Visual Calculus: Verical Asymptotes
This site discusses how to find vertical asymptotes and their graphs.
Oregon State University
Calculus Quest: Exponential Functions
This CalculusQuest site provides a basic introduction to exponential functions, covering the laws of exponents and exponential growth and decay. At the bottom of the page are links to exponential equations, exercises, and the...
National Council of Teachers of Mathematics
The Math Forum: Ask Dr. Math: Horizontal and Vertical Asymptotes
Dr. Math answers 'why would a line cross a horizontal asymptote?'.
University of Saskatchewan (Canada)
University of Saskatchewan: Moderate Rational Function Problems
A set of exercises of moderate difficulty on rational functions, complete with solutions and hints for students..