Question

Complete the following to describe the translations from the parent function for the given function

Answer 1

The parent function is given by

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

The transformed function is given by

`y=-2\sqrt[3]{x+3}-7`

Reflection:

Notice that the transformed function is being multiplied with a negative sign.

This is a reflection over the x-axis.

Stretch/Compression:

Notice that the transformed function is being multiplied with a scale factor of 2 which is greater than 1.

Therefore, it is a vertical stretch of 2.

Horizontal translation:

Notice that the transformed function is being translated to the left by 3 units.

Therefore, this is a horizontal translation to the left by 3 units.

Vertical translation:

Notice that the transformed function is being translated downward by 7 units.

Therefore, this is a vertical translation down by 7 units.