Use the image to answer the question.

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 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 .

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 .

GPT-4o mini · Answer

To accurately describe the graph of $ f(x) $ based on the information you provided, I would need to see the graph in question. However, I can help you understand how to determine the average rate of change of a function over an interval. The average rate of change of a function $ f(x) $ over an interval $[a, b]$ is calculated using the formula: $$ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} $$ This rate can be negative if $ f(b) < f(a) $, meaning the function is decreasing over that interval. Here’s how you can analyze the average rate of change across the given intervals: 1. Check the values of $ f(x) $ at the endpoints of each interval (for example, at $ x = 0 $ and $ x = 1 $ for the interval [0,1]). 2. Determine whether the function is increasing or decreasing on each interval by comparing the values. 3. Based on this analysis, you can select the appropriate response from the options given. If you can provide a description or key features of the graph, I can help you determine which statements are correct.