Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 3

Topic

Special Functions

Description

This example showcases the creation of a table of x-y coordinates and the graphing of the function y = ∛(-2x). The graph displays a curve with labeled points at specific coordinates, including (-2, 1.587), (-1, 1.259), (0, 0), (1, -1.259), and (2, -1.587). This visual representation helps students understand how the negative coefficient -2 affects the cube root function.

Cube root functions are an essential topic in advanced algebra and precalculus. They belong to the family of radical functions and possess unique properties that distinguish them from other functions. This collection of examples offers a comprehensive look at various forms of cube root functions, enabling students to grasp their characteristics and behaviors under different transformations.

Presenting multiple worked-out examples is crucial for students to fully comprehend cube root functions. By examining different variations and transformations of these functions, students can develop a deeper intuition about their properties, such as their shape, domain, range, and how they respond to different coefficients and constants, including negative values.

Teacher's Script: Let's analyze this function and compare it to the previous two examples. How does the negative coefficient -2 inside the cube root affect the graph? Notice how the curve is now a reflection of the previous example. Can you explain why this happens? What would you expect if we used -1 instead of -2?

For a complete collection of math examples related to Cube Root Functions click on this link: Math Examples: Cube Root Functions Collection.