Question

Question

Use the image to answer the question.

A coordinate plane for f of x versus x.

Describe the graph of f(x)
by selecting the correct statement.

(1 point)
Responses

The average rate of change is negative on the interval [0,1]
and on the interval [3,4]
.
The average rate of change is negative on the interval left bracket 0 comma 1 right bracket and on the interval left bracket 3 comma 4 right bracket .

The average rate of change is negative on the interval [1,3]
and also on the interval [6,7]
.
The average rate of change is negative on the interval left bracket 1 comma 3 right bracket and also on the interval left bracket 6 comma 7 right bracket .

The average rate of change is negative only on the interval [6,7]
.
The average rate of change is negative only on the interval left bracket six comma seven right bracket .

The average rate of change is negative only on the interval [1,3]
.
The average rate of change is negative only on the interval left bracket 1 comma 3 right bracket .
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Answer 1

To accurately answer your question about the graph of \( f(x) \) based on the average rate of change in the specified intervals, I would need to analyze the image you're referencing. Since I don't have access to visual content, I can't determine the behavior of the graph directly.

However, I can explain how to find the average rate of change for a function and how to interpret it:

1. Average Rate of Change Formula: The average rate of change of \( f(x) \) over an interval \([a, b]\) is given by: \[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]

2. Interpreting the Rate:

   • If the average rate of change is positive, the graph is increasing over the interval.
   • If it's negative, the graph is decreasing over that interval.
   • A rate of change of zero indicates that the function is constant over that interval.

You should check the values of \( f(x) \) at the specified points in each interval to see whether \( f(x) \) is increasing or decreasing, thus allowing you to determine the average rate of change for the intervals given.

Please examine the intervals mentioned and apply the formula to see which statements are true based on the graph you have.