Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 23

Topic

Special Functions

Description

This example features a graph for the function y = ∛(-2x) - 1 along with a table listing x-y coordinates. The graph displays points such as (-2, 0.587), (-1, 0.259), (0, -1), (1, -2.259), and (2, -2.587). This visual representation helps students understand how combining a negative coefficient inside the cube root with a negative constant outside affects the function's behavior.

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 reflections and vertical 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 complex combinations of transformations.

Teacher's Script: Let's analyze this function that combines multiple transformations. How does multiplying x by -2 inside the cube root and subtracting 1 outside change the graph compared to the original function y = ∛x? Notice how the curve is reflected horizontally and shifted downward. Can you explain why this happens? What would you expect if we used positive coefficients instead?

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