Question

Use the following graph of the function f(x) = x3 − 3x2 − x + 3 to answer this question:

What is the average rate of change from x = −1 to x = 3?
-3
-1
0
3

Answer 1

let me know it this helps if not try mathway or another algebra website 

Answer 2

the average rate of change is equal to
`0`

Explanation:

we have

`f(x)=x^(3)-3x^(2)-x+3` -----> a cubic function

For
`x=-1`

The value of f)x) is equal to

`f(-1)=0` -----> see the graph

For
`x=3`

The value of f(x) is equal to

`f(3)=0` -----> see the graph

so

we know that

the average rate of change using the graph is equal to

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

In this problem we have

`f(a)=f(-1)=0`

`f(b)=f(3)=0`

`a=-1`

`b=3`

Substitute

`(0-0)/(3+1)=0`