The function g(x)=(x-2^2. the function f(x)=g(x) +3 the function f(x) is shifted horizontally how many places to where ? the function f(x) is shifted vertically how many places where ?

The parent function is:
 y = x ^ 2
 Applying the following function transformation we have:
 Horizontal translations:
 Suppose that h> 0
 To graph y = f (x-h), move the graph of h units to the right.
 We have then:
 g (x) = (x-2) ^ 2
 Then, we have the following function transformation:
 Vertical translations
 Suppose that k> 0
 To graph y = f (x) + k, move the graph of k units up.
 We have then that the original function is:
 g (x) = (x-2) ^ 2
 Applying the transformation we have
 f (x) = g (x) +3
 f (x) = (x-2) ^ 2 + 3
 
 the function f(x)  moves horizontally 2 units rigth.
 The function f (x) is shifted vertically 3 units up.

Wow. that is a really cool question.