Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 1

Topic

Rational Functions

Description

This math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / x. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph is a hyperbola with branches in the first and third quadrants, illustrating the characteristic shape of this basic rational function.

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 rational functions' behavior.

Seeing multiple worked-out examples is essential for students to fully grasp 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 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 first example of a rational function. We're looking at y = 1 / x, which is one of the simplest forms of a rational function. Notice how the graph forms a hyperbola that never touches the x or y axes. These lines that the graph approaches but never reaches are called asymptotes. Can you identify where these asymptotes are located? As we go through more examples, pay attention to how changes in the function affect the position and shape of the hyperbola.

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