Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 24

Topic

Rational Functions

Description

This math example focuses on creating a table of x-y coordinates and graphing 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, -0.667), (-1.5, -0.6), (0, 0), (1.5, -3), and (2, -2). The graph is plotted on a grid, illustrating how subtracting constants both in the denominator and from the entire fraction affects the graph's shape and position.

Rational functions are crucial for understanding algebraic concepts such as asymptotes and transformations. This collection provides visual examples that help students see how different constants impact rational function graphs. By examining several examples, students can better understand how these transformations shift or reflect graphs.

Multiple worked-out examples are essential for students to master rational functions fully. Each example introduces slight changes that result in different behaviors for the graphs, helping students develop pattern recognition skills for predicting transformations based on equations.

Teacher's Script: Now let's look at our twenty-fourth example: y = (-1) / (x - 1) - 1. How does this function differ from previous ones? Notice that we are subtracting constants from both parts of the equation. What effect do you think these changes will have on the graph? As you observe it, try to explain why it behaves this way compared to similar functions we've studied before.

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