Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 12

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 - 1). The image presents both the table of x-y coordinates and the resulting graph. The graph includes points labeled at specified coordinates, demonstrating how the negative signs in both the numerator and denominator, along with the constant, affect the graph's shape and position.

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 combinations of signs and constants can result in diverse graph shapes and positions. By examining multiple examples, students can identify patterns and develop a deeper understanding of rational functions' behavior and transformations.

Presenting multiple worked-out examples is crucial for students to fully comprehend the concept of rational functions and their transformations. Each example builds upon the previous ones, introducing different combinations of signs and constants that result in unique graph shapes and positions. This approach enhances students' analytical skills and improves their ability to recognize and predict the effects of various transformations on rational functions.

Teacher's Script: Now, let's analyze our twelfth example: y = -1 / (-x - 1). How does this function compare to our previous examples? Notice that we have negative signs in both the numerator and denominator, as well as a subtraction in the denominator. What effect do you think this will have on the graph? As you observe the graph, can you explain why it's positioned and shaped the way it is? How does it compare to y = 1 / (x + 1)? As we continue exploring more examples, try to predict how combinations of negative signs and constants will affect the graphs.

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