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A graph shows an increasing function that curves upward in quadrant one. The horizontal axis is labeled x and the vertical axis is labeled y.

What is the average rate of change of the function graphed on the interval x:[1,3]
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(1 point)
Responses

−1
negative 1

26
26

6
6

13

1 answer

To find the average rate of change of a function over an interval, we use the formula:

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

where \( f(a) \) and \( f(b) \) are the function values at the endpoints \( a \) and \( b \) of the interval.

Given the interval \( x: [1, 3] \):

  • Let \( a = 1 \) and \( b = 3 \).
  • Determine \( f(1) \) and \( f(3) \) from the graph.

Assuming you have the corresponding \( y \)-values at \( x = 1 \) and \( x = 3 \):

  • Let's say \( f(1) = y_1 \) and \( f(3) = y_3 \).

Then substituting into the formula:

\[ \text{Average Rate of Change} = \frac{f(3) - f(1)}{3 - 1} = \frac{y_3 - y_1}{2} \]

Without the specific \( y \)-values from the graph, I can't calculate the exact average rate of change. However, you can apply this method using the actual \( y \)-values from the graph: substitute those values into the formula to get the answer.

Once you calculate \( \frac{y_3 - y_1}{2} \), you can select the closest answer from the given options.