Question

the function y = f(x) is graphed below. plot a line segment connecting the points on f where x = -8 and x = -6. use the line segment to determine the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -6. plot a line segment by clicking in two locations. click a segment to delete it.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$. Here, $a=-8$ and $b = - 6$.

Step2: Estimate function values

Suppose from the graph, $f(-8)=y_1$ and $f(-6)=y_2$. We need to read the $y$ - values corresponding to $x=-8$ and $x = - 6$ from the graph. Let's assume $f(-8) = 4$ and $f(-6)=8$.

Step3: Calculate average rate of change

Substitute into the formula: $\frac{f(-6)-f(-8)}{-6-(-8)}=\frac{8 - 4}{-6 + 8}=\frac{4}{2}=2$.

Answer:

2