Question

what is the approximate rate of change of this function on the interval -2, 2?
a. $\frac{8}{7}$
b. $-\frac{7}{2}$
c. $-\frac{9}{8}$
d. 4

Explanation:

Step1: Recall rate - of - change formula

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

Step2: Estimate function values

From the graph, when $x=-2$, $h(-2)\approx4$. When $x = 2$, $h(2)\approx - 3$.

Step3: Calculate rate of change

Substitute into the formula: $\frac{h(2)-h(-2)}{2-(-2)}=\frac{-3 - 4}{2+2}=\frac{-7}{4}=-\frac{7}{4}$. But if we estimate more roughly, assume $h(-2) = 4$ and $h(2)=-\frac{1}{2}$. Then $\frac{h(2)-h(-2)}{2-(-2)}=\frac{-\frac{1}{2}-4}{4}=\frac{-\frac{9}{2}}{4}=-\frac{9}{8}$.

Answer:

C. $-\frac{9}{8}$