Question

Use the image to answer the question.

A coordinate plane for f of x versus x.
▼Click for Long Desc
The x-axis ranges from 0 to 6 in increments in unit increments. The vertical axis represents f of x ranging from negative 2 to 3 in unit increments. A line passes through the coordinates left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 1 comma 1 right parenthesis, left parenthesis 3 comma 0 right parenthesis, left parenthesis 4 comma negative 0 point 5 right parenthesis, left parenthesis 5 comma negative 0 point 5 right parenthesis, and left parenthesis 6 comma 0 right parenthesis.

Given the graph of f(x)
, on which interval is the average rate of change the greatest?

(1 point)

The function has the greatest average rate of change over the interval [5,6]
.

The function has the greatest average rate of change over the interval [0,1]
.

The function has the greatest average rate of change over the interval [4,5]
.

The function has the greatest average rate of change over the interval [1,4]
.

Answer 1

Compute the average rate = [f(b) − f(a)]/(b − a):

- [5,6]: (0 − (−0.5))/(6−5) = 0.5
- [0,1]: (1 − 2/3)/(1−0) = 1/3 ≈ 0.333
- [4,5]: (−0.5 − (−0.5))/(5−4) = 0
- [1,4]: (−0.5 − 1)/(4−1) = −1.5/3 = −0.5

The greatest average rate of change is 0.5 on [5,6].