Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 39

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 displays a curve with specific points plotted, including (-2, -1), (-1, -1.794), (0, -2), (1, -2.145), and (2, -2.259). This visual representation helps students understand how negating the cube root, including a fractional coefficient and constant inside, and subtracting a 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, stretches, horizontal shifts, 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 both inside and outside the cube root.

Teacher's Script: Let's analyze this function that combines multiple transformations. How does negating the cube root of (0.5x + 1) and subtracting 1 change the graph compared to the original function y = ∛x? Notice how the curve is reflected vertically, stretched horizontally, shifted horizontally, and shifted downward. 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.