[WILL GIVE BRAINLIEST IF CORRECT]

f(x) = |x| and g(x) = |x| + 3
The transformation applied to get the graph of g(x) from the graph of f(x) is:

A.) a vertical transformation of 3 units upward
B.) a vertical transformation of 3 units downward
C.) a horizontal transformation of 3 units to the left
D.) a horizontal transformation of 3 units to the right

Respuesta :

It's a y translation. So vertical transformation of 3 units upward.
The parent graph is y = absolute value of x.  If there is side-to-side movment it would be reflected inside the absolute value signs with the x, like Ix - 3I, for example.  That tells us that the parent graph moves 3 units to the right.  We have no number inside the absolute value signs with the x, so that means that there is no horizontal movement at all.  The +3 outside the absolute value signs indicate vertical movement.  Since the 3 is positive, the shift is up 3.  So your answer is A.) a vertical transformation of 3 units upward.