Ask a New Question
Menu

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 [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] .

1 answer

To accurately describe the graph of \( f(x) \) and determine the correct statement regarding the intervals where the average rate of change is negative, we would need to analyze the function visually or have the function's values provided.

Here's how to interpret the statements based on intervals:

  • Average Rate of Change: The average rate of change of a function \( f(x) \) on an interval \([a, b]\) is given by the formula: \[ \frac{f(b) - f(a)}{b - a} \] If this value is negative, it indicates that \( f(x) \) is decreasing over that interval.

If we consider each response:

  1. If the average rate of change is negative on the intervals \([0,1]\) and \([3,4]\), then the graph must be decreasing in these ranges.
  2. If it's negative on \([1,3]\) and \([6,7]\), then the graph is decreasing in those ranges.
  3. If it's only negative on \([1, 3]\), then that section is the only decreasing part of the graph.
  4. Similarly for \([6,7]\).

To select the correct response, one would need to confirm whether the function is indeed decreasing in those specified intervals of the x-axis.

Based on the phrasing of the response options, the most precise way to answer would depend on the nature of the function. Unfortunately, without the function or specific values/graph provided, it's impossible to select the correct statement definitively.

If you have a specific function in mind or a graph to analyze, please provide that, and I can help you identify the correct average rate of change across the intervals.