Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 17

Topic

Special Functions

Description

This example illustrates the creation of a table of x-y coordinates and the graphing of the function y = ∛(2x + 1) + 1. The graph displays a curve with specific points plotted, including (-2, -0.442), (-1, 0), (0, 2), (1, 2.442), and (2, 2.710). This visual representation helps students understand how combining a coefficient and a horizontal shift inside the cube root with a vertical shift 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 stretches, shifts, and combinations thereof.

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.

Teacher's Script: Let's analyze this function that combines multiple transformations. How does multiplying x by 2 and adding 1 inside the cube root, and then adding 1 outside change the graph compared to the original function y = ∛x? Notice how the curve is stretched horizontally, 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.