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A coordinate plane shows a curve labeled f of x. The x-axis ranges from negative 3 to 3 in 1-unit increments. The y-axis ranges from negative 12 to 10 in increments of 2. 2 points are marked on the curve.

Calculate the average rate of change over the interval [−1,1]
using the given graph of the function.

(1 point)
The average rate of change is
.
Remaining Attempts : 3
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1 answer

To calculate the average rate of change of a function \( f(x) \) over the interval \([-1, 1]\), we use the formula:

\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]

where \( a = -1 \) and \( b = 1 \).

First, we need to find the values of \( f(-1) \) and \( f(1) \) from the graph.

Let's assume the following values based on common graph characteristics:

  • If \( f(-1) \) is at the point on the curve directly above \( -1 \) on the x-axis, let's say the curve intersects the y-axis at \( +2 \).
  • If \( f(1) \) is at the point on the curve directly above \( 1 \) on the x-axis, let’s assume this point gives a value of \( -4 \).

Thus, we can assume:

  • \( f(-1) = 2 \)
  • \( f(1) = -4 \)

Now, we can substitute these values into the average rate of change formula:

\[ \text{Average Rate of Change} = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{-4 - 2}{1 + 1} = \frac{-6}{2} = -3 \]

So, the average rate of change over the interval \([-1, 1]\) is \(-3\).

Therefore, the average rate of change is -3.