Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 13

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 provided shows both a table of x-y coordinates and the corresponding graph of the function. The table contains specific x-y coordinates: (-2, 0), (-1.5, -1), (0, 2), (1.5, 1.4), (2, 1.333), which are plotted on the graph. This example illustrates how adding a constant to a rational function affects its graph.

Rational functions are a crucial topic in algebra and calculus, representing the ratio of two polynomial functions plus a constant in this case. This collection of examples helps teach this topic by providing visual representations of various rational functions, allowing students to see how changes in the function affect its graph. By examining multiple examples, students can identify patterns and develop a deeper understanding of how constants added to rational functions shift the graph vertically.

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 helps students develop pattern recognition skills and enhances their ability to predict the behavior of rational functions based on their equations.

Teacher's Script: Let's examine our thirteenth example of a rational function: y = 1 / (x + 1) + 1. Notice how this function is similar to y = 1 / (x + 1), but with an additional constant at the end. How does this change affect the graph? You'll see that the hyperbola has shifted upward by one unit. Can you explain why this happens? As we continue with more examples, pay attention to how adding constants in different parts of the function affects 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.