Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 3

Topic

Rational Functions

Description

This math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (-x). The image presents both the table of x-y coordinates and the resulting graph. Interestingly, the graph is identical to that of y = -1 / x, showing a hyperbola with branches in the second and fourth quadrants. This example demonstrates how different forms of rational functions can produce the same graph.

Rational functions are a fundamental concept in algebra and calculus, representing the ratio of two polynomial functions. This collection of examples supports the teaching of this topic by providing visual representations of various rational functions, enabling students to observe how different forms of equations can result in similar graphs. By examining multiple examples, students can identify patterns and develop a deeper understanding of rational functions' behavior and equivalence.

Presenting multiple worked-out examples is crucial for students to fully comprehend the concept of rational functions. Each example builds upon the previous ones, introducing different forms of equations that may result in similar or different graph shapes and characteristics. This approach enhances students' analytical skills and improves their ability to recognize equivalent forms of rational functions.

Teacher's Script: Let's examine our third example: y = 1 / (-x). At first glance, this function might seem different from our previous example, y = -1 / x. However, when we graph it, we see that it produces the same hyperbola in the second and fourth quadrants. Why do you think this happens? Can you explain how these two functions are equivalent? As we continue with more examples, try to identify when different forms of equations might produce the same graph.

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