Math Example--Special Functions--Cube Root Functions in Tabular and Graph Form: Example 38

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 displays a curve with specific points plotted, including (-2, -2.709), (-1, -2.442), (0, -2), (1, 0), and (2, 0.442). This visual representation helps students understand how negating the cube root, including a negative coefficient and constant inside, and subtracting a constant 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, horizontal shifts, and vertical shifts.

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 both inside and outside the cube root.

Teacher's Script: Now, let's examine this function that combines multiple transformations. How does negating the cube root of (-2x + 1) and subtracting 1 change the graph compared to the original function y = ∛x? Notice how the curve is reflected vertically and horizontally, compressed 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.