Answer
Net Change: $h^2 + 2h + 2ah$
Average Rate of change: $h + 2 + 2a$
Work Step by Step
From the equation $g(x) = (x+1)^2$, we are looking from the net change and average rate of change from x=a to x=a+h
At x=a, $f(x) = (a+1)^2$
At x=a+h, $f(x) = (a+h+1)^2$
Net Change: $f(a+h) - f(a) = a^2 + h^2 + 1 + 2a + 2h + 2ah - (a^2 + 2a + 1) = h^2 + 2h + 2ah$
Average Rate of change: $\frac{f(a+h)- f(a)}{(a+h)-(a)} = \frac{h^2 + 2h + 2ah}{h} = h + 2 + 2a$
