Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 4

Topic

Special Functions

Description

This example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = ∛(0.5x). The graph displays a curve with labeled points at specific coordinates, including (-2, -1), (-1, -0.794), (0, 0), (1, 0.794), and (2, 1). This visual representation helps students understand how a fractional coefficient like 0.5 affects the cube root function.

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 fractional coefficients.

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 different coefficients, including fractions and whole numbers.

Teacher's Script: Now, let's examine this function with a fractional coefficient. How does multiplying x by 0.5 inside the cube root change the graph compared to the original function y = ∛x? Notice how the curve is less steep. Can you explain why this happens? What would you expect if we used 0.25 instead of 0.5?

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