Math Example--Rational Concepts--Graphs of Rational Functions: Example 4

Topic

Rational Functions

Description

This example presents the graph of the rational function y = 1 / (x - 4). The graph is a hyperbola with a vertical asymptote at x = 4. 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 crucial 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, we see that the vertical asymptote has shifted to x = 4. This shift is due to the subtraction of 4 in the denominator. Observe how the function approaches infinity as x approaches 4 from both sides. Understanding how changes in the function equation affect the graph's position and behavior 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.