Select the function that represents the transformation of the parent function three units to the left and up two.

f (x) = |x - 3| - 2

f (x) = - |x - 3| + 2

f (x) = |x + 3| + 2

f (x) = - |x + 3| + 2

The third.

When you have a number in the parentheses (abs value function in this case) that is applied to the x value of the graph in the negative way. Since the 3 is positive, the graph will move to the left (negative) 3 spaces. Outside of the parentheses is the opposite; since the two is positive, it will move two places up, resulting in C being the only possible answer.

The reason it isn't D is because adding a negative to the front of the function would flip it over an axis which is not something we want to do here.