Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 5

Topic

Rational Functions

Description

This math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / (x + 1). The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph is a hyperbola with points marked at specific coordinates, illustrating how the addition of a constant in the denominator affects the graph's position.

Rational functions are a crucial topic in algebra and calculus, representing the ratio of two polynomial functions. 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 in the denominator shift the graph horizontally.

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 fifth example of a rational function: y = 1 / (x + 1). Notice how this function is similar to y = 1 / x, but with a slight change in the denominator. How does this change affect the graph? You'll see that the hyperbola has shifted to the left by one unit. Can you explain why this happens? As we continue with more examples, pay attention to how adding or subtracting 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.