Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 16

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 negating the numerator of a rational function and subtracting a constant affects its graph.

Rational functions are a crucial topic in algebra and calculus, representing the ratio of two polynomial functions with additional transformations. 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 negations and constants influence rational functions' behavior.

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 combinations of changes 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: Now, let's analyze our sixteenth example: y = -1 / (x + 1) - 1. How does this function compare to our previous examples? Notice that we've negated the numerator and subtracted 1 from the entire fraction. What effect do you think these changes will have on the graph? As you observe the graph, can you explain why it's positioned and shaped the way it is? How does it compare to y = 1 / (x + 1) - 1? As we continue exploring more examples, try to predict how combinations of negations 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.