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...
CK-12 Foundation
Horizontal and Vertical Asymptotes: Rational Functions
Play with the graph of a rational function to discover the asymptote patterns. Young scholars use the interactive lesson to discover the relationship between the asymptotes and the function. As they manipulate the function, the graph...
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.
Virginia Department of Education
Rational Functions: Intercepts, Asymptotes, and Discontinuity
Discover different patterns by making connections between a rational function and its graph. An engaging lesson asks scholars to explore the behavior of different rational functions. Groups discover a connection between the function and...
Flipped Math
Calculus AB/BC - Infinite Limits and Vertical Asymptotes
Infinite limits just got infinitely more interesting. The 15th of 18 installments in Unit 1 - Limits and Continuity looks at infinite limits and vertical asymptotes of rational functions. Scholars review how to determine the locations of...
CK-12 Foundation
Oblique Asymptotes: Rational Functions and Asymptotes
Examine the connection between rational functions and their graphs. Individuals use an online manipulative to sort equations with horizontal and oblique asymptotes. They focus on the degree of the numerator and denominator.
CK-12 Foundation
Infinite Limit Type: Asymptotes and End Behavior Question
There are an infinite number of reasons to use the resource. Scholars drag vertical and horizontal lines to the graph of a rational function to identify all asymptotes. They investigate the connection between asymptotes and limits to...
Flipped Math
Calculus AB/BC - Limits at Infinity and Horizontal Asymptotes
Learning about end behavior means it's close to the end of the unit. The 16th of 18 lessons in Unit 1 - Limits and Continuity has scholars watch a video to learn how limits at infinity can be used to determine horizontal asymptotes and...
Curated OER
Asymptotes and Zeros
Learn how to explore rational functions and investigate the graphs rational functions and identify its singularities and asymptotes. Students approximate the solutions to rational equations and inequalities by graphing.
Curated OER
Vertical Asymptotes: M=N and M=N+1
In this algebra worksheet, learners 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.
Curated OER
Rational Functions
Through a mini assessment, students identify and list the vertical and horizontal asymptotes for the given rational functions and determine the type of asymptote of a given rational function. They also decide which form of a function...
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
Hyperbolas: Sketching from the Equation
In this algebra worksheet, young scholars sketch graphs of hyperbolas after solving equations to standard form and interpreting the center, vertices, foci, axis, asymptotes, and eccentricity from the equation. There are 58 questions.
Curated OER
Graph, Identify Asymptotes, Find Domain and Range, for Eleven Simple Rational Functions
Using this worksheet, pupils graph 11 simple rational functions. They also find asymptotes, domain, and range for each function. The solutions are provided.
Curated OER
Exploring Vertical Asymptotes
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...
Balanced Assessment
Getting Closer
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...
Curated OER
Crossing the Asymptote
Pupils investigate graphs and their asymptotes. In this precalculus instructional activity, students examine the numerator and denominator of their rational functions. This helps them identify where and when the graph will cross its...
Curated OER
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 worksheet contains...
Curated OER
Worksheet 28 - Functions
In 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.
Curated OER
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.
CK-12 Foundation
Infinite Limit Type: Properties of Limits
Limits can provide some valuable information about graphs. A slider interactive lets learners see the behavior of a graph around asymptotes. They investigate relationships between limits and asymptotes.
CK-12 Foundation
Horizontal Translations or Phase Shifts: Tangent
Patterns can be shifty! Find the pattern when shifting the graph of tangent. Pupils move the graph of tangent to different locations on the coordinate plane. They observe what happens to the function and its vertical asymptotes before...
CK-12 Foundation
Analyzing the Graphs of Functions: Analyzing a Rational Function
Shift the function and transform the key features of the graph. By translating the graph of the rational function, class members find out how the key features alter. Pupils determine the domain, range, asymptotes, and intervals of...
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...
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