given the function f(x) = x^2 - 5x + 0, determine the average rate of change of the function over the…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-3$, $b = 9$, and $f(x)=x^{2}-5x$.

Step2: Calculate $f(a)$

Substitute $x=-3$ into $f(x)$: $f(-3)=(-3)^{2}-5\times(-3)=9 + 15=24$.

Step3: Calculate $f(b)$

Substitute $x = 9$ into $f(x)$: $f(9)=9^{2}-5\times9=81-45 = 36$.

Step4: Calculate the average rate of change

$\frac{f(9)-f(-3)}{9-(-3)}=\frac{36 - 24}{9 + 3}=\frac{12}{12}=1$.

Answer:

$1$