Question

1. the graph of y = h(x) is shown. find the average rate of change of h on -3,2.

Explanation:

Step1: Recall the average - rate - of - change formula

The average rate of change of a function $y = h(x)$ on the interval $[a,b]$ is given by $\frac{h(b)-h(a)}{b - a}$, where $a=-3$ and $b = 2$.

Step2: Identify $h(a)$ and $h(b)$ from the graph

From the graph, when $x=-3$, $h(-3)=-2.4$ and when $x = 2$, $h(2)=-5.4$.

Step3: Substitute values into the formula

Substitute $a=-3$, $b = 2$, $h(-3)=-2.4$ and $h(2)=-5.4$ into the formula $\frac{h(b)-h(a)}{b - a}$. We get $\frac{h(2)-h(-3)}{2-(-3)}=\frac{-5.4-(-2.4)}{2 + 3}$.

Step4: Simplify the expression

First, simplify the numerator: $-5.4-(-2.4)=-5.4 + 2.4=-3$. Then, the denominator is $2+3 = 5$. So, $\frac{-3}{5}=-0.6$.

Answer:

$-0.6$