Question

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

Answer 1

Answer:

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

Step-by-step 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 $f(x)=|x+4|+2$

Answer 2

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