Question

The function
`f(x)=\sqrt[3]{x+4}` is transformed to
`g(x) = \sqrt[3]{x-1} +3`

What transformations are performed from function f to function g?

Choose the answers that are correct:

1. Function f is translated up 3 units.


2. Function f is translated to the right 5 units.


3. Function f is translated to the right 3 units.


4. Function f is translated down 1 unit.

Answer 1

A) Function f is translated up 3 units.

B) Function f is translated to the right 5 units.

Explanation:

Given functions:

`f(x)=\sqrt[3]{x+4}`

`g(x)=\sqrt[3]{x-1}+3`

To transform function f to function g, first subtract 5 from the x:

`\begin{aligned}f(x-5)&=\sqrt[3]{x-5+4}\\&=\sqrt[3]{x-1}\end{aligned}`

Now add 3 to the function:

`f(x-5)+3=\sqrt[3]{x-1}+3`

When a number "n" is subtracted from the x variable of a function, the function is translated "n" units to the right.

When a number "n" is added to a function, the function is translated "n" units up.

Therefore, the transformations performed from function f to function g are:

• Function f is translated to the right 5 units.
• Function f is translated up 3 units.