Math Example--Rational Concepts--Graphs of Rational Functions: Example 21

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = -(x - 5) / (x - 4). The graph features a vertical asymptote at x = 4, which is correctly labeled. Students are tasked with graphing the function and determining its vertical asymptote.

Rational functions are a significant 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

As we examine this graph, notice the vertical asymptote at x = 4. This occurs where the denominator equals zero. Observe how the negative sign affects the graph's orientation. Pay attention to how the function approaches negative infinity as x approaches 4 from the left, and positive infinity as x approaches 4 from the right. Also, note how the numerator being (x - 5) instead of (x - 4) affects the graph's behavior. 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.