Compare the domain, range, graph, and critical values on the graph of [math]y = −4 \sqrt[3]{x} + 2[/math] to the graph of [math]y = \sqrt[3]{x}[/math]. How are these differences reflected in the algebraic equations?
[list=1] [*]Determine the domain and range of [math]y = \sqrt[3]{x}[/math]. [*]Find at least three points on the graph of [math]y = \sqrt[3]{x}[/math], including any critical points. [*]Plot the points and graph [math]y = \sqrt[3]{x}[/math]. [*]Determine the domain of [math]y = −4 \sqrt[3]{x} + 2[/math]. [*]Determine the range of [math]y = −4 \sqrt[3]{x} + 2[/math]. [*]Find at least three points on the function [math]y = −4 \sqrt[3]{x} + 2[/math], including critical points. [*]Plot the points and graph [math]y = −4 \sqrt[3]{x} + 2[/math] on the same coordinate plane as the graph of [math]y = \sqrt[3]{x}[/math]. [*]Compare the domains and ranges of the functions [math]y = \sqrt[3]{x}[/math] and [math]y = −4 \sqrt[3]{x} + 2[/math]. Note how the equation is related to any differences between the domains and ranges. [*]Compare the critical points of [math]y = \sqrt[3]{x}[/math] and [math]y = −4 \sqrt[3]{x} + 2[/math], and note how the equation is related to the differences between these points. [*]Compare the general shapes of [math]y = \sqrt[3]{x}[/math] and [math]y = −4 \sqrt[3]{x} + 2[/math], and note how the equation is related to the differences. [/list]