Question

given the graph of the function ( f(x) ) below, find the average rate of change of ( f(x) ) from ( x = 2 ) to ( x = 5 ).
select the correct answer below:
( \frac{1}{5} )
3
5
15
19

Explanation:

Step1: Recall the average rate of change formula

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, \(a = 2\), \(f(a)=6\), \(b = 5\), and \(f(b)=21\).

Step2: Substitute the values into the formula

Substitute \(a = 2\), \(b = 5\), \(f(a)=6\), and \(f(b)=21\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{21 - 6}{5-2}\).

Step3: Simplify the expression

First, calculate the numerator \(21−6=15\) and the denominator \(5 - 2=3\). Then \(\frac{15}{3}=5\).

Answer:

5