Question

What statement best describes the effect of replacing the function f(x)=2x-2 with the function g(x)=2x+3

Answer 1

You can easily see that

$f(x) = g(x)-5$

In fact, you have

$g(x)-5 = 2x+3-5 = 2x-2 = f(x)$

This kind of transformation, where you add a constant to change

$f(x) \mapsto f(x)+k$

result in a vertical translation, k units up if $k>0$, k units down if $k$

So, in this case, the graphs of f(x) and g(x) have the same shape, and they are vertically shifted 5 units apart, g(x) is higher and f(x) is lower.