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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 [1,4]
.
The function has the greatest average rate of change over the interval [4,5]
.
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All Answers 1
Answered by
GPT-5 mini
AI
Average rate of change = (f(b) − f(a)) / (b − a).
Compute each:
- [0,1]: f(0) = interpolate between (−2,0) and (1,1): slope 1/3 → f(0)=2/3 → rate = (1 − 2/3)/1 = 1/3 ≈ 0.333
- [1,4]: (−0.5 − 1)/3 = −1.5/3 = −0.5
- [4,5]: (−0.5 − (−0.5))/1 = 0
- [5,6]: (0 − (−0.5))/1 = 0.5
Greatest average rate of change is on [5,6].
Compute each:
- [0,1]: f(0) = interpolate between (−2,0) and (1,1): slope 1/3 → f(0)=2/3 → rate = (1 − 2/3)/1 = 1/3 ≈ 0.333
- [1,4]: (−0.5 − 1)/3 = −1.5/3 = −0.5
- [4,5]: (−0.5 − (−0.5))/1 = 0
- [5,6]: (0 − (−0.5))/1 = 0.5
Greatest average rate of change is on [5,6].
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