Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 28

Topic

Special Functions

Description

This example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = ∛(− 2x + 1) − 1. The graph is annotated with specific points on the curve, illustrating how combining a negative coefficient and a horizontal shift inside the cube root with a vertical shift outside affects the function's behavior.

Cube root functions are a crucial 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 reflections, stretches, and shifts in multiple directions.

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 complex combinations of transformations.

Teacher's Script: Now, let's examine this function that combines multiple transformations. How does multiplying x by -2 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, compressed horizontally, 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.