## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$7$
Average rate of change from $a$ to $b$: $=\dfrac{f(b)-f(a)}{b-a}$ Wth $a=1$ and $b=3$: \begin{aligned} f(b)=f(3) &=3(3)^{2}-5(3) \\ &=3(9)-15 \\ &=27 - 15 \\ &=12 \\ \\f(a)=f(1) &=3(1)^{2}-5(1) \\ &=3-5 \\ &=-2\\ \\\text{substituting these values in the rate of change formula above yields}\\ \\&=\frac{12-(-2)}{3-1} \\ \\&=\frac{14}{2} \\ \\&=7\end{aligned}