Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 23

Topic

Rational Functions

Description

This math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = (-1) / (x - 1) + 1. The image shows both a table of x-y coordinates and the corresponding graph. The table includes points such as (-2, 1.333), (-1.5, 1.4), (0, 2), (1.5, -1), and (2, 0). The graph is plotted on a grid, illustrating how subtracting a constant in the denominator and adding a constant to the entire fraction affects the graph's shape and position.

Rational functions are an important concept in algebra and calculus, representing the ratio of two polynomial functions with additional transformations. This collection of examples aids in teaching this topic by providing visual representations of various rational functions, allowing students to observe how alterations in the function impact its graph. By studying multiple examples, students can identify patterns and develop a comprehensive understanding of how constants affect rational functions.

Seeing multiple worked-out examples is essential for students to fully grasp the concept of rational functions and their transformations. Each example builds upon the previous ones, introducing slight variations in the function that result in different graph shapes and positions. This approach enhances students' ability to predict the behavior of rational functions based on their equations.

Teacher's Script: Let's examine our twenty-third example: y = (-1) / (x - 1) + 1. How does this function compare to previous examples? Notice that we are subtracting a constant in the denominator and adding a constant to the entire fraction. What effect do you think these changes will have on the graph? As you observe the graph, can you explain why it behaves this way? How does it compare to y = (-1) / (x - 1)? As we continue with more examples, pay attention to how constants affect the position and shape of the 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.