Question

If the graph of the function g defined by g(x)=x^2+1 is translated vertically upward by 4 units, it becomes the graph of a function ff(x)

Answer 1

Why not draw the two graphs in question? The imagery may well answer this question for you.

Notice that in g(x)=x^2+1, g(x) is also the y-value, whereas x is the horizontal coordinate. Thus, you're not going to be changing either x or x^2, but you will have to chance that '+1' in the given function.