Question

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

Parent function y=∛x
Shift 9 units to the left.
Shift horizontally by a factor of 5.
Reflect across the x-axis.

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)}`