which function has the greater rate of change from -1, 8? rate of change for h(x): rate of change for m(x)…

Explanation:

Step1: Recall rate - of - change formula

The rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$.

Step2: Calculate rate of change for $h(x)$

From the graph of $h(x)$, when $x=-1$, assume $h(-1)= - 3$ (estimated from the graph), when $x = 8$, assume $h(8)=2$ (estimated from the graph). Then the rate of change of $h(x)$ over $[-1,8]$ is $\frac{h(8)-h(-1)}{8-(-1)}=\frac{2 - (-3)}{9}=\frac{2 + 3}{9}=\frac{5}{9}\approx0.56$.

Step3: Calculate rate of change for $m(x)$

Given $m(-1)=-4$ and $m(8)=0.5$. The rate of change of $m(x)$ over $[-1,8]$ is $\frac{m(8)-m(-1)}{8-(-1)}=\frac{0.5-(-4)}{9}=\frac{0.5 + 4}{9}=\frac{4.5}{9}=0.5$.

Answer:

rate of change for $h(x)$: $\frac{5}{9}$ rate of change for $m(x)$: $0.5$ Which function is steeper on the given interval? $h(x)$