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

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}). Here, (a = 3) and (b = 5).

Step2: Find ( f(3) ) and ( f(5) ) from the graph

From the graph, we need to determine the ( y )-values (function values) at ( x = 3 ) and ( x = 5 ). Let's assume from the graph (by looking at the coordinates) that at ( x = 3 ), ( f(3)= - 8 ) and at ( x = 5 ), ( f(5)=4 ) (we need to check the grid, each square is likely 1 unit. Let's confirm: when ( x = 3 ), the point is at ( y=-8 ); when ( x = 5 ), the point is at ( y = 4 )).

Step3: Substitute into the formula

Now, substitute ( a = 3 ), ( b = 5 ), ( f(3)=-8 ) and ( f(5) = 4 ) into the average rate of change formula: [ \frac{f(5)-f(3)}{5 - 3}=\frac{4-(-8)}{5 - 3}=\frac{4 + 8}{2}=\frac{12}{2}=6 ]

Answer:

The average rate of change is ( 6 ).