Math Example--Rational Concepts--Graphs of Rational Functions: Example 2

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = -1 / x. The graph is a hyperbola with vertical and horizontal asymptotes, with the vertical asymptote at x = 0. Students are asked to graph the function and identify its vertical asymptote.

Rational functions are an important area of study in algebra, involving fractions of polynomial functions. This collection of examples aids in teaching the topic by providing visual representations of various rational functions, allowing students to observe how changes in the function affect its graph. By examining multiple examples, students can recognize patterns and develop a deeper understanding of asymptotes and function behavior.

Exposure to multiple worked-out examples is crucial for students to fully comprehend mathematical concepts. It allows them to encounter different scenarios, reinforces key ideas, and helps develop problem-solving skills. This repetitive exposure can increase confidence and enhance overall understanding of rational functions.

Teacher's Script

Now, let's compare this graph to our previous example of y = 1 / x. Notice how the negative sign has flipped the graph, but the vertical asymptote remains at x = 0. Observe how the function approaches negative infinity as x approaches zero from the right, and positive infinity as x approaches zero from the left. Understanding these nuances is essential for mastering rational functions.

For a complete collection of math examples related to Rational Functions click on this link: Math Examples: Graphs of Rational Functions Collection.