Question

Find the average rate of change of the function f(x), represented by the graph, over the interval [-4, -1]. Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula . The value of f(-1) is . The value of f(-4) is . The average rate of change of f(x) over the interval [-4, -1] is .

Answer 1

The answer to the blanks in the prompt are as follows:

- The formula is
`$(f(b)-f(a))/(b-a)$`

- The value of f(-1) is 2

- The value of f(-4) is 9

- The average rate of change of f(x) over the interval [-4,-1] is
`$(11)/(3)$`

The average rate of change of a function over an interval is the slope of the secant line that intersects the graph of the function at the interval's endpoints.

The formula for the average rate of change of the function f over the interval [a, b] is:

`(f(b)-f(a))/(b-a)`

In the case of the graph you sent, the function f is represented by a blue line, and the interval is [4,1]. The y-values of the endpoints of the interval are f(-4)=9 and f(-1)=2.

Therefore, the average rate of change of f over the interval [4,1] is:

`(f(-1) f(-4))/(1-(-4))=(2-9)/(1+4)=(11)/(3)`T

he average rate of change of the function is
`$(11)/(3)$`, which means that the function is decreasing at an average rate of
`$(11)/(3)$` units per unit change in x.

Answer 2

2

Explanation:

We are given that a graph which represents f(x).

Interval:[-4,-1]

We have to find the average rate of change of the function f(x).

From the graph we can see that

f(-4)=-3

f(-1)=3

We know that the average rate of change of the function

Average rate =
`(f(b)-f(a))/(b-a)`

Using the formula

Average rate of change of f=
`(3-(-3))/(-1-(-4))`

Average rate of change of f=
`(6)/(3)=2`