Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 30

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) - 1. The graph is plotted on a Cartesian plane with labeled points. This visual representation helps students understand how combining a negative fractional coefficient and a constant inside the cube root with a negative constant outside affects the function's behavior.

Cube root functions are an essential 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, stretches, horizontal shifts, and vertical shifts.

Presenting 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 both inside and outside the cube root.

Teacher's Script: Let's analyze this function that combines multiple transformations. How does multiplying x by -0.5 and adding 1 inside the cube root, and then subtracting 1 outside change the graph compared to the original function y = ∛x? Notice how the curve is reflected horizontally, stretched, and shifted both horizontally and vertically. 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.