Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 2

Topic

Special Functions

Description

This example illustrates the creation of a table of x-y coordinates and the graphing of the function y = ∛(2x). The graph displays a curve with plotted 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 coefficient 2 affects the cube root function.

Cube root functions are a crucial topic in advanced algebra and precalculus. They belong to the family of radical functions and exhibit unique properties that set them apart from other functions. This collection of examples provides a comprehensive look at various forms of cube root functions, helping students grasp their characteristics and behaviors under different transformations.

Providing multiple worked-out examples is essential 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.

Teacher's Script: Now, let's compare this function to the previous one. How does multiplying x by 2 inside the cube root change the graph? Notice the steeper curve compared to y = cube root of x. Can you predict what would happen if we used a fraction instead of 2? How would that affect the graph's shape?

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