Math Example--Rational Concepts--Graphs of Rational Functions: Example 8

Topic

Rational Functions

Description

This example presents the graph of the rational function y = 1 / (-9x + 3). The graph is plotted on a grid with a vertical asymptote at x = 1/3, marked by a dashed red line. Students are asked to graph the function and identify its vertical asymptote.

Rational functions are a key topic 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 essential for students to fully comprehend mathematical concepts. It enables 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

In this example, notice that the vertical asymptote is at x = 1/3. This can be found by solving -9x + 3 = 0. Observe how the negative coefficient in the denominator affects the graph's orientation compared to previous examples. The function approaches negative infinity as x approaches 1/3 from the left, and positive infinity as x approaches 1/3 from the right. Understanding these nuances and how they relate to the function's equation is crucial 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.