the function ( y = f(x) ) is graphed below. what is the average rate of change of the function ( f(x) ) on…

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function (y = f(x)) on the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}). Here, (a = 1) and (b=2).

Step2: Find (f(1)) and (f(2)) from the graph

From the graph, when (x = 1), (y=f(1)=5) (since the point ((1,5)) lies on the graph of (y = f(x))), and when (x = 2), (y = f(2)=7) (since the point ((2,7)) lies on the graph of (y = f(x))).

Step3: Substitute values into the formula

Substitute (a = 1), (b = 2), (f(1)=5), and (f(2)=7) into the formula (\frac{f(b)-f(a)}{b - a}). We get (\frac{f(2)-f(1)}{2 - 1}=\frac{7 - 5}{2-1}).

Step4: Simplify the expression

(\frac{7 - 5}{2-1}=\frac{2}{1}=2).

Answer:

(2)