Answer
Net change: $2ah+2h+h^{2}$
Average rate of change: $2a+2+h$
Work Step by Step
We find the net change from $x=a$ to $x=a+h$:
$g(a+h)-g(a)=(a+h+1)^{2}-(a+1)^{2}=(a^2+ah+a+ha+h^2+h+a+h+1)-(a^2+2a+1)=2ah+2h+h^{2}$
Next we find the average rate of change for this interval:
$\frac{g(a+h)-g(a)}{a+h-a}=\frac{2ah+2h+h^{2}}{h}=\frac{h(2a+2+h)}{h}=2a+2+h$
