Average Rate of Change Practice

Question

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Question
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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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Answer 1

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

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

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

From the graph, you will observe the y-values at the points \( f(-1) \) and \( f(1) \).

1. Identify the value of the function at \( x = -1 \) (let's say it's \( y_1 \)).
2. Identify the value of the function at \( x = 1 \) (let's say it's \( y_2 \)).

Then, plug these values into the formula:

\[ \text{Average Rate of Change} = \frac{y_2 - y_1}{1 - (-1)} = \frac{y_2 - y_1}{2} \]

Once you have the specific values from the graph for \( y_1 \) and \( y_2 \), you can calculate the average rate of change. If you can provide the specific y-values at those points, I can help you with the calculation!