Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 2

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. The image showcases both the table of x-y coordinates and the resulting graph. The graph is a hyperbola with branches in the second and fourth quadrants, illustrating how the negative sign affects the function's shape compared to the previous example.

Rational functions are an important concept in algebra and calculus, representing the ratio of two polynomial functions. 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 rational functions' behavior.

The importance of presenting multiple worked-out examples cannot be overstated when it comes to students fully grasping the concept of rational functions. Each example builds upon the previous one, introducing slight variations in the function that result in different graph shapes and characteristics. This approach enhances students' pattern recognition skills and improves their ability to predict the behavior of rational functions based on their equations.

Teacher's Script: Now, let's look at our second example: y = -1 / x. Notice how this function is similar to our first example, but with a negative sign. How does this change affect the graph? You'll see that the hyperbola now appears in the second and fourth quadrants instead of the first and third. What do you think causes this shift? As we continue with more examples, try to predict how changes in the equation will affect the graph's appearance.

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