Asymptote Teacher Resources

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...

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...

Students 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...

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...

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.

Budding mathematicians graph given functions, identify the asymptotes, graph absolute values, and write a table of points. This three-page worksheet contains 23 problems.

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.

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...

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...

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...

In this slant asymptote worksheet, students solve 1 rational equation.  Students determine the slant asymptote of a rational equation.

For 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.

Calculating average speeds is not as simple as finding an average. The instructional activity introduces class members to rational functions by presenting a problem about finding an average speed for the rest of a trip. Pupils develop an...

In this infinite limit worksheet, students compute horizontal and vertical asymptotes. They use trigonometric functions to find the limits of functions and compare results. This two-page worksheet contains examples and explanations and...

In this graphing functions worksheet, 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...

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...

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...

In this conic sections worksheet, students solve and complete 17 various types of problems. First, they write the conics in standard form and graph. Then, students determine the equation that best represents each description that...

For this hyperbola worksheet, students solve and complete 33 different problems that include identifying various hyperbolas. First, they graph each hyperbola, stating the center, vertices, co-vertices, foci, asymptotes, and latus rectum....

In this graphs of functions instructional activity, 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...

Where do those asymptotes come from? Learners graph, simplify, and solve rational functions in the fifth module of a 10-part series. Beginning with graphing, pupils determine the key characteristics of the graphs including an in-depth...

In this slant asymptotes activity, students calculate the slant asymptotes in four rational functions.  The solutions are not provided.

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,...

For this evaluating limits worksheet, learners 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....