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Question

A coordinate plane for f of x versus x.

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 [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 [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 [4,5].
The function has the greatest average rate of change over the interval left bracket 4 comma 5 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 .
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Answer 1

To determine which interval has the greatest average rate of change based on the graph of $f(x)$ versus $x$, we would typically look at the slopes of the secant lines over the given intervals. The average rate of change of a function $f(x)$ over an interval $[a,b]$ is calculated using the formula:

$$\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}$$

From the options presented, you would need to analyze the graph of $f(x)$ over the intervals $[0,1]$, $[5,6]$, $[4,5]$, and $[1,4]$ to see where the greatest difference in $f(x)$ values occurs relative to the length of each interval.

Without seeing the graph, I can't ascertain which interval actually has the greatest average rate of change. However, you can find this by calculating or estimating the average rate of change for each option based on the $f(x)$ values you see.

If you are looking for the correct response, please evaluate the intervals using the graph data you have and determine which one has the highest slope or average rate of change.