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

Shift 4 units left.

Shift 2 units up.

A. g(x) = \x - 41 + 2

B. g(x) = x + 21 - 4

C. g(x) = [X + 4 + 2

D. g(x) = x + 2 + 4

C) g(x) =  |x+4|+2

The new function  g(x) =  |x+4|+2

Step-by-step explanation:

Given that the parent function f(x) = |x|

The function shifts '4' units left then the function transformed to

g(x) = |x+4|

Again the function shift '2' units up then the function transformed to

g(x) = |x+4|+2

Final answer:-

The new function g(x) =  |x+4|+2

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).