Question

The graph shows the function f(x).

Which value is closest to the average rate of change from x = 1 to x = 4?




A.−3.5

​ B.−2.3

​​ C. −1.4

​​D .−0.3

Answer 1

Option B is correct

-2.3

Explanation:

Average rate of change(A(x)) for the function f(x) over the interval [a, b] is given by:

`A(x) = (f(b)-f(a))/(b-a)` ....[1]

We have to find the average rate of change from x = 1 to x = 4.

From the graph as shown below

For x = 1

f(1) = 3

and

For x = 4

f(4) = -3.9

Using [1] we have;

`A(x) = (f(4)-f(1))/(4-1)`

Substitute the given values we have;

`A(x) = (-3.9-3)/(3)`

⇒
`A(x) = (-6.9)/(3)`

Simplify:

`A(x) = -2.3`

Therefore, -2.3 value is closest to the average rate of change from x = 1 to x = 4