Question

question 1
use the graph of ( f(x) ) to evaluate the following:
the average rate of change of ( f ) from ( x = 0 ) to ( x = 5 ) is
give your answer as an integer or reduced fraction.
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Explanation:

Step1: Identify the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) from \(x=a\) to \(x = b\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 0\) and \(b=5\).

Step2: Find \(f(0)\) and \(f(5)\) from the graph

From the graph, when \(x = 0\), \(f(0)=1\). When \(x = 5\), \(f(5)=3\).

Step3: Substitute values into the formula

Substitute \(a = 0\), \(b = 5\), \(f(0)=1\), and \(f(5)=3\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{f(5)-f(0)}{5-0}=\frac{3 - 1}{5}\).

Step4: Simplify the fraction

\(\frac{3 - 1}{5}=\frac{2}{5}\).

Answer:

\(\frac{2}{5}\)