Math Example--Rational Concepts--Graphs of Rational Functions: Example 10

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = (x - 5) / (x + 4). The graph features a vertical asymptote at x = -4 and displays two branches, one in the first quadrant and one in the third quadrant. Students are asked to graph the function and identify 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 crucial 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 that the vertical asymptote is at x = -4, where the denominator equals zero. Observe how the function has two distinct branches, one in the first quadrant and one in the third quadrant. This behavior is similar to our previous example but with different positioning. Pay attention to how the constants in the numerator and denominator affect the graph's position and shape. Understanding these relationships is key to 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.