Math Example--Rational Concepts--Graphs of Rational Functions: Example 9

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = (x + 3) / (x + 2). The graph features a vertical asymptote at x = -2 and shows two branches, one in the second quadrant and one in the fourth quadrant. Students are tasked with graphing the function and determining its vertical asymptote.

Rational functions are a fundamental topic in algebra, involving fractions of polynomial functions. This collection of examples facilitates teaching the topic by providing visual representations of various rational functions, enabling students to observe how changes in the function affect its graph. By studying multiple examples, students can identify patterns and develop a deeper understanding of asymptotes and function behavior.

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

Teacher's Script

Let's analyze this graph carefully. Notice that the vertical asymptote is at x = -2, which is where the denominator equals zero. Observe how the function has two distinct branches, one in the second quadrant and one in the fourth quadrant. This behavior is different from our previous examples and is due to the linear terms in both the numerator and denominator. Understanding how the structure of the rational function affects its graph is crucial for mastering this topic.

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