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

Explanation:

Step1: Identify the formula for average rate of change

The formula for 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=-7) and (b = - 5).

Step2: Find (f(-7)) and (f(-5)) from the graph

From the graph, when (x=-7), (y = f(-7)=4) (since the point ((-7,4)) lies on the graph). When (x=-5), (y=f(-5)=14) (since the point ((-5,14)) lies on the graph).

Step3: Substitute values into the formula

Substitute (a=-7), (b=-5), (f(a) = 4), and (f(b)=14) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{14 - 4}{-5-(-7)}=\frac{10}{2}).

Answer:

(5)