Answer
$7$
Work Step by Step
General formula for average rate of change from x to y: $\frac{f(y)-f(x)}{y-x}.$ Hence here: $\frac{f(3)-f(1)}{3-1}=\frac{(3\cdot3^2-5\cdot3)-(3\cdot1^2-5\cdot1)}{2}=\frac{(3\cdot9-15)-(3\cdot1-5)}{2}=\frac{(27-15)-(3-5)}{2}=\frac{14}{2}=7.$