Question

the graph of a function h is shown below. use the graph of the function to find its average rate of change from x = -1 to x = 5. simplify your answer as much as possible.

Explanation:

Step1: Find the values of \( h(-1) \) and \( h(5) \)

From the graph, when \( x=-1 \), \( h(-1)= - 3 \); when \( x = 5 \), \( h(5)=8 \).

Step2: Use the average - rate - of - change formula

The average rate of change formula is \( \frac{h(b)-h(a)}{b - a} \), where \( a=-1 \), \( b = 5 \).
Substitute the values into the formula: \( \frac{h(5)-h(-1)}{5-(-1)}=\frac{8-(-3)}{5 + 1} \).
Simplify the numerator and denominator: \( \frac{8 + 3}{6}=\frac{11}{6} \).

Answer:

\( \frac{11}{6} \)