Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 5

Topic

Special Functions

Description

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

Cube root functions are an important 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, including negative fractional coefficients.

Providing 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, including negative fractions.

Teacher's Script: Let's analyze this function with a negative fractional coefficient. How does multiplying x by -0.5 inside the cube root change the graph compared to the previous examples? Notice how the curve is both less steep and reflected across the y-axis. Can you explain why this happens? How does this graph compare to y = ∛(0.5x)?

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