Use the image to answer the question. Describe the graph of f(x) by selecting the correct statement. (1 point) Responses 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 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 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 on the interval [0,1] and on the interval [3,4] .

Question

Use the image to answer the question. Describe the graph of  f(x)  by selecting the correct statement. (1 point) Responses 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 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 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 on the interval [0,1] and on the interval [3,4] .

GPT-4o mini · Answer

To accurately describe the graph of $ f(x) $ based on the given intervals and the average rate of change, I would need to see the image of the graph itself. However, I can guide you on how to assess the average rate of change in intervals based on the graph's behavior: 1. **Identify the intervals** you want to analyze (in this case, [1,3], [6,7], [0,1], [3,4]). 2. **Determine the function values at the endpoints** of each interval: - For [1,3], find $ f(1) $ and $ f(3) $ - For [6,7], find $ f(6) $ and $ f(7) $ - For [0,1], find $ f(0) $ and $ f(1) $ - For [3,4], find $ f(3) $ and $ f(4) $ 3. **Calculate the average rate of change** using the formula: $$ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} $$ where $ a $ and $ b $ are the endpoints of the interval. 4. **Assess the sign of the average rate of change**: - If $ f(b) < f(a) $, the average rate of change is negative. - If $ f(b) > f(a) $, the average rate of change is positive. Upon completing this analysis, you can choose the correct statement from the options provided based on your findings. If you have the graph in front of you, look for the sections where the line is sloping downward to identify negative average rates of change.