Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 6

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). The image showcases both the table of x-y coordinates and the resulting graph. The graph displays a hyperbola with labeled points on the curve, illustrating how the negative sign in the numerator and the constant in the denominator affect the graph's shape and position.

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 how negative signs and constants influence 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 and their transformations. Each example builds upon the previous ones, introducing combinations of changes in the function that result in different graph shapes and positions. 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 sixth example: y = -1 / (x + 1). How does this function compare to our previous example? Notice that we've added a negative sign in the numerator. What effect do you think this will have on the graph? As you observe the graph, you'll see that it's not only shifted to the left like our previous example, but it's also reflected over the x-axis. Can you explain why this reflection occurs? 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.