Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 21

Topic

Special Functions

Description

This example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = ∛(x) - 1. The graph displays a curve with specific points plotted, including (-2, -2.259), (-1, -2), (0, -1), (1, 0), and (2, 0.259). This visual representation helps students understand how subtracting a constant outside the cube root affects the function's behavior.

Cube root functions are a vital 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, including vertical shifts.

Offering 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 vertical translations.

Teacher's Script: Now, let's examine how subtracting a constant term affects the cube root function. How does subtracting 1 from the cube root of x change the graph compared to y = ∛x? Notice how the entire curve is shifted downward by 1 unit. Can you predict what would happen if we added 1 instead? How would that affect the graph's position?

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