Answer to Question #169111 in Algebra for william

Question

In Desmos:

Describe the transformations applied to the parent f(x)= ³sqaure root of x into the new equation f(x)=-³sqaure root of x into the new equation f(x) = - ³sqaure root of x-5-3

Answer 1

Solution.

$y=\sqrt[3]{x}$ (blue line)

$y=-\sqrt[3]{x}$ - symmetry about the x-axis (green line)

$y=-\sqrt[3]{x-5}$ - parallel transfer by 5 units to the right (purple line)

$y=-\sqrt[3]{x-5}-3$ - parallel transfer by 3 units down (red line)