Question

what is the average rate of change of the function from $x = 1$ to $x = 3$?
10
12.5
15
30

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) from \(x=a\) to \(x = b\) is given by \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 1\), \(b=3\). From the graph, when \(x = 1\), \(y=f(1)=10\) and when \(x = 3\), \(y=f(3)=30\).

Step2: Substitute values into the formula

Substitute \(a = 1\), \(b = 3\), \(f(a)=10\), \(f(b)=30\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{30 - 10}{3-1}=\frac{20}{2}\).

Step3: Simplify the expression

\(\frac{20}{2}=10\).

Answer:

10