Question

Use the image to answer the question.

A curve with 3 points is plotted on a coordinate plane. The x-axis ranges from negative 1 to 3 and the y-axis ranges from negative 1 to 5, both by 1-unit increments. the graph goes up from 0 to 1, then then to far 2.

Use the average rate of change to describe the graph of f(x) over the interval [1,4] .

(1 point)
Responses

The average rate of change is −1/3.
The average rate of change is negative Start Fraction 1 over 2 End Fraction .

The average rate of change is 3.
The average rate of change is 3.

The average rate of change is 1/3.
The average rate of change is Start Fraction 1 over 2 End Fraction .

The average rate of change is 1
.
The average rate of change is 1.
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1 answer

To find the average rate of change of a function \( f(x) \) over the interval \([1, 4]\), we need to determine the values of \( f(1) \) and \( f(4) \). The formula for the average rate of change is given by:

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

where \( a = 1 \) and \( b = 4 \).

Since I don’t have the actual image of the graph you referenced, I'll guide you on how to calculate it based on the provided information about the graph:

  1. Identify the value of \( f(1) \) and \( f(4) \) from the graph.
  2. Apply these values into the formula.

For example, if from the graph, we find:

  • \( f(1) = 2 \) (as an arbitrary value)
  • \( f(4) = 3 \) (as another arbitrary value)

We would calculate it as follows:

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

Assuming your graph depicts values differently, replace \( f(1) \) and \( f(4) \) with the actual values from your graph to derive the correct average rate of change.

Once you find the average rate of change using your graph, match your answer with the provided responses.