Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 7

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 specific points highlighted, illustrating how the negative sign and constant in the denominator affect the graph's shape and 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 and negative signs in the denominator shift and reflect the graph.

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 seventh example of a rational function: y = 1 / (-x + 1). Notice how this function is similar to y = 1 / x, but with some changes in the denominator. How do these changes affect the graph? You'll see that the hyperbola has shifted and reflected. Can you explain why this happens? As we continue with more examples, pay attention to how adding constants and negative signs 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.