Question

question the function y = f(x) is graphed below. plot a line segment connecting the points on f where x = 4 and x = 6. use the line segment to determine the average rate of change of the function f(x) on the interval 4 ≤ 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, $a = 4$ and $b=6$.

Step2: Estimate function values from the graph

We need to estimate $f(4)$ and $f(6)$ from the graph. Suppose from the graph, $f(4)\approx - 10$ and $f(6)\approx20$.

Step3: Calculate the average rate of change

Substitute $a = 4$, $b = 6$, $f(4)\approx - 10$ and $f(6)\approx20$ into the formula $\frac{f(b)-f(a)}{b - a}$. We get $\frac{f(6)-f(4)}{6 - 4}=\frac{20-(-10)}{2}=\frac{20 + 10}{2}=\frac{30}{2}=15$.

Answer:

15