question the function y = f(x) is graphed below. plot a line segment connecting the points on f where x = -1…

question the function y = f(x) is graphed below. plot a line segment connecting the points on f where x = -1 and x = 4. use the line segment to determine the average rate of change of the function f(x) on the interval -1 ≤ x ≤ 4. plot a line segment by clicking in two locations. click a segment to delete it. answer attempt 1 out of 2 you must answer all questions above in order to submit.

question the function y = f(x) is graphed below. plot a line segment connecting the points on f where x = -1 and x = 4. use the line segment to determine the average rate of change of the function f(x) on the interval -1 ≤ x ≤ 4. plot a line segment by clicking in two locations. click a segment to delete it. answer attempt 1 out of 2 you must answer all questions above in order to submit.

Answer

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, $a=-1$ and $b = 4$.

Step2: Estimate function values from the graph

From the graph, when $x=-1$, assume $f(-1)=-8$ (by looking at the $y$-coordinate of the point on the graph where $x = - 1$). When $x = 4$, assume $f(4)=-16$ (by looking at the $y$-coordinate of the point on the graph where $x = 4$).

Step3: Calculate the average rate of change

Substitute $a=-1$, $b = 4$, $f(-1)=-8$ and $f(4)=-16$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(4)-f(-1)}{4-(-1)}=\frac{-16-(-8)}{4 + 1}=\frac{-16 + 8}{5}=\frac{-8}{5}=-1.6$.

Answer:

$-1.6$