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

Answer

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 ).