Question

consider the graph. what is the average of change on the interval ( 2 leq x leq 5 )

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( y = f(x) \) over the interval \( [a, b] \) is given by \( \frac{f(b) - f(a)}{b - a} \).

Step2: Identify the points

From the graph, we have two points: when \( x = 2 \), \( y = 3 \) (so the point is \( (2, 3) \)) and when \( x = 5 \), \( y = 24 \) (so the point is \( (5, 24) \)). Here, \( a = 2 \), \( f(a)=3 \), \( b = 5 \), and \( f(b)=24 \).

Step3: Substitute into the formula

Substitute the values into the average rate of change formula:
\[
\frac{f(5)-f(2)}{5 - 2}=\frac{24 - 3}{5 - 2}
\]

Step4: Simplify the numerator and denominator

First, calculate the numerator: \( 24 - 3 = 21 \). Then, calculate the denominator: \( 5 - 2 = 3 \). So we have \( \frac{21}{3} \).

Step5: Divide

Divide 21 by 3: \( \frac{21}{3}=7 \).

Answer:

7