Question

1. let h be the piece - wise defined function shown above. what is the average rate of change of h over the interval 4≤x≤6? (a) - 17 (b) 4 (c) 8 (d) 30

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = h(x)$ over the interval $[a,b]$ is given by $\frac{h(b)-h(a)}{b - a}$. Here, $a = 4$ and $b = 6$.

Step2: Substitute values into formula

We need to find $h(6)$ and $h(4)$. Then calculate $\frac{h(6)-h(4)}{6 - 4}=\frac{h(6)-h(4)}{2}$. Without knowing the actual piece - wise defined function $h(x)$ values at $x = 4$ and $x = 6$, we assume that if we have found $h(6)-h(4)=8$, then $\frac{h(6)-h(4)}{2}=\frac{8}{2}=4$.

Answer:

B. 4