Question

If you apply the changes below to the absolute value parent function f(x)=lxl, what is the equation of the new function?

Shift 4 units left
Shift 2 units up

Answer 1

Answer: The equation of the new function is
`f(x)=|x+4|+2.`

Step-by-step explanation: We are given to find the equation of the new function if we apply the following changes to the absolute value parent function f(x)=lxl :

Shift 4 units left and Shift 2 units up.

We know that

if we shift the absolute value parent function f(x) = |x| to h units left and k units up, then the new equation will be

`f(x)=|x+h|+k.`

Therefore, if the function is shifted 4 units left and 2 units up, then the equation of the new function will be

`f(x)=|x+4|+2.`

Thus, the equation of the new function is
`f(x)=|x+4|+2.`

Answer 2

`f(x)=|x+4|+2`

Explanation:

The given absolute value function is

`f(x)=|x|`

This is the base or the parent function.

The transformation
`f(x)=|x+b|+c` will shift the parent function b units to the left and c units up.

From the question, b=4 units and c=2 units.

The new equation is
`f(x)=|x+4|+2`