Math Example--Rational Concepts--Graphs of Rational Functions: Example 15

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = (x + 4) / ((x + 2)(x - 5)). The graph features vertical asymptotes at x = -2 and x = 5, demonstrating the behavior of the function near these asymptotes. Students are tasked with graphing the function and determining its vertical asymptotes.

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 the two vertical asymptotes at x = -2 and x = 5, which occur where the denominator equals zero. Observe how the function approaches positive or negative infinity as it nears each asymptote. Pay attention to how the numerator affects the overall shape of the graph, particularly between the asymptotes. Understanding these complex behaviors and their relationship to the function's equation is crucial for mastering rational functions with multiple factors in the denominator.

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