Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 10

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 + 1). The graph displays a curve with points plotted at specific x-values, including (-2, 1.259), (-1, 1.144), (0, 1), (1, 0.794), and (2, 0). This visual representation helps students understand how combining a negative fractional coefficient with a positive constant inside the cube root affects the 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 both horizontal stretches and shifts.

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 combinations of transformations inside the cube root.

Teacher's Script: Let's analyze this function with transformations inside the cube root. How does multiplying x by -0.5 and adding 1 inside the cube root change the graph compared to the original function y = cube root of x? Notice how the curve is reflected, stretched horizontally, and shifted to the right. Can you explain the effect of each transformation separately? How do they work together to produce this final graph?

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