Lesson Plan
EngageNY

#### Horizontal and Vertical Asymptotes of Graphs of Rational Functions

For Teachers 11th - 12th Standards
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...
Interactive
CK-12 Foundation

#### Horizontal and Vertical Asymptotes: Rational Functions

For Students 9th - 12th Standards
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...
Lesson Plan
Curated OER

#### Worksheet 7 - Asymptote

For Teachers Higher Ed
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.
Lesson Plan
1
1
Virginia Department of Education

#### Rational Functions: Intercepts, Asymptotes, and Discontinuity

For Students 10th - 12th Standards
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...
AP Test Prep7:55
1
1
Flipped Math

#### Calculus AB/BC - Infinite Limits and Vertical Asymptotes

For Students 10th - 12th
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...
Interactive
CK-12 Foundation

#### Oblique Asymptotes: Rational Functions and Asymptotes

For Students 9th - 12th Standards
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.
Interactive
CK-12 Foundation

#### Infinite Limit Type: Asymptotes and End Behavior Question

For Students 11th - Higher Ed Standards
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...
AP Test Prep13:27
1
1
Flipped Math

#### Calculus AB/BC - Limits at Infinity and Horizontal Asymptotes

For Students 10th - 12th
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...
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.  Students approximate the solutions to rational equations and inequalities by graphing.
Worksheet
Curated OER

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

For Students 9th - 12th
In this algebra worksheet, 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.
Lesson Plan
Curated OER

#### Rational Functions

For Teachers 9th - 12th Standards
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...
Lesson Plan
Texas Instruments

#### Graphs of Rational Functions

For Teachers 9th - 12th Standards
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...
Lesson Plan
Curated OER

#### Hyperbolas: Sketching from the Equation

For Teachers 9th - Higher Ed
In this algebra worksheet, students 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.
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.
Lesson Plan
Curated OER

#### Exploring Vertical Asymptotes

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

#### Crossing the Asymptote

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

#### Worksheet 28 - Functions

For Teachers Higher Ed
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.
Worksheet
Curated OER

#### Senior Analysis: Graphing Rational Functions

For Students 10th - 12th
Budding mathematicians graph given functions, identify the asymptotes, graph absolute values, and write a table of points. This three-page worksheet contains 23 problems.
Interactive
CK-12 Foundation

#### Infinite Limit Type: Properties of Limits

For Students 11th - Higher Ed Standards
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.
Interactive
CK-12 Foundation

#### Horizontal Translations or Phase Shifts: Tangent

For Students 10th - 12th Standards
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...
Interactive
CK-12 Foundation

#### Analyzing the Graphs of Functions: Analyzing a Rational Function

For Students 11th - Higher Ed
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...
Lesson Plan
EngageNY

#### Graphing Rational Functions

For Teachers 11th - 12th Standards
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...