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use the graph of ( f(x) ) to evaluate the following:
the average rate of change of ( f ) from ( x = 0 ) to ( x = 4 ) is ( \frac{1}{4} ) ×
give your answer as an integer or reduced fraction.
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Explanation:

Answer:

To find the average rate of change of \( f(x) \) from \( x = 0 \) to \( x = 4 \), we use the formula for average rate of change:

\[
\text{Average rate of change} = \frac{f(4) - f(0)}{4 - 0}
\]

Step 1: Find \( f(0) \)

From the graph, when \( x = 0 \), \( f(0) = 1 \).

Step 2: Find \( f(4) \)

From the graph, when \( x = 4 \), \( f(4) = 5 \).

Step 3: Calculate the average rate of change

Substitute \( f(4) = 5 \), \( f(0) = 1 \), and \( 4 - 0 = 4 \) into the formula:

\[
\text{Average rate of change} = \frac{5 - 1}{4 - 0} = \frac{4}{4} = 1
\]

The average rate of change of \( f \) from \( x = 0 \) to \( x = 4 \) is \( \boldsymbol{1} \).