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)
Responses

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 left bracket 5 comma 6 right bracket .

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

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 left bracket 0 comma 1 right bracket .

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

Answer 1

Compute the average rate of change (slope) for each interval:

- [5,6]: (f(6)-f(5))/(6-5) = (0 - (-0.5))/1 = 0.5
- [1,4]: (f(4)-f(1))/(4-1) = (-0.5 - 1)/3 = -0.5
- [0,1]: f(0) is on the line between (-2,0) and (1,1), so f(0)=2/3. Then (1 - 2/3)/1 = 1/3 ≈ 0.333...
- [4,5]: (f(5)-f(4))/1 = (-0.5 - (-0.5)) = 0

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