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
Vertical Asymptotes: M=N and M=N+1
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.
Curated OER
Exploring Vertical Asymptotes
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...
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...
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...
CK-12 Foundation
Basic Trigonometric Limits: Evaluating Limits of tan(x)
Chase a periodic moving limit. Learners graphically determine the limit of the tangent function at different input values. Using sliders, pupils find out whether the tangent function approaches the same value from the left and the right....
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...
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...
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.
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
Rational Functions
Through a mini assessment, learners 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...
Curated OER
Graphing Rational Functions
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,...
Curated OER
Graphing a Rational Function
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.
Curated OER
Rational Expressions/Equations Test
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.
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
Graphing Rational Functions
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.
Concord Consortium
Rational and Not So Rational Functions
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...
Curated OER
The Canoe Trip, Variation 2
The behavior of a rational function near a vertical asymptote is the focus around this trip up a river. Specifically, numerical and graphical understanding is studied. The canoe context pushes the variables as numbers, rather than as...
Curated OER
Rational Functions
In this college level Pre-Calculus worksheet students evaluate rational functions, identify the domain, vertical asymptotes, and x- and y-intercepts. The three page worksheet contains forty problems. Answers are provided.
Curated OER
Graphing Functions
In this graphing functions instructional activity, 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...
Curated OER
Simplifying Functions
In this simplifying functions learning exercise, 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,...
Mt. San Antonio Collage
Graphs of Rational Functions
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.
Curated OER
Limits at Infinity and Horizontal Asymptotes
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...