If you apply the changes below to the absolute value parent function, f(x) = |x|, which of these is the equation of the new function? Shift 2 units to the left Shift 3 units down

Question

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

1. Shift 2 units to the left
2. Shift 3 units down

A. g(x) = |x+3| - 2

B. g(x) = |x-2| - 3

C. g(x) = |x+2| - 3

D. g(x) = |x-3| - 2

Answer 1

The easiest way of understanding this is to try graphing these in a graphing program like Desmos.

You can see the differences in the shifts.

Remember that the values on the inside of the absolute value signs shift the function left or right, the opposite of what the sign is. If it's x+1 it will shift LEFT 1 unit. then the value outside the absolute value sign is the vertical shift. if it's +1 then up 1, -4 then down four.