Question

Write a function based on the given parent function and the transformations in the given order.

Answer 1

Given the function

$y= \sqrt[3]{x}$

A shift 9 units to the left will result in the function:

$y'= \sqrt[3]{x+9}$

A Shrink horizontally by a factor of 5 will result in the function:

$y''=\sqrt[3]{5(x+9)}$

A reflection across the x-axis will result in the function

$y'''=-\sqrt[3]{5(x+9)}$

Therefore, the final function after the series of transformation is

$y'''=-\sqrt[3]{5(x+9)}$