Math Example--Rational Concepts--Graphs of Rational Functions: Example 11

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = (x - 1) / (x - 3). The graph features a vertical asymptote at x = 3 and displays two distinct branches, one in the first quadrant and another in the third quadrant. Students are tasked with graphing the function and identifying its vertical asymptote.

Rational functions are a crucial 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

Let's analyze this graph carefully. Notice the vertical asymptote at x = 3, which occurs where the denominator equals zero. Observe how the function approaches positive infinity as x approaches 3 from the right, and negative infinity as x approaches 3 from the left. The two branches in the first and third quadrants show how the function behaves in different regions of the coordinate plane. Understanding these characteristics and their relationship 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.