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

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-6 \\leq x \\leq -3$?

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-6 \\leq x \\leq -3$?

Answer

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function ( f(x) ) on the interval ([a, b]) is given by (\frac{f(b) - f(a)}{b - a}). Here, ( a=-6 ) and ( b = - 3 ).

Step2: Find ( f(-6) ) and ( f(-3) ) from the graph

From the graph, when ( x=-6 ), we look at the point on the graph. Let's assume from the graph (by identifying the coordinates) that ( f(-6)=10 ) (since at ( x = - 6 ), the ( y )-value is 10) and when ( x=-3 ), ( f(-3)=-20 ) (since at ( x=-3 ), the ( y )-value is - 20).

Step3: Substitute into the formula

Substitute ( a=-6 ), ( b = - 3 ), ( f(-6)=10 ) and ( f(-3)=-20 ) into the formula (\frac{f(b)-f(a)}{b - a}).

We get (\frac{f(-3)-f(-6)}{-3-(-6)}=\frac{-20 - 10}{-3 + 6}=\frac{-30}{3}=-10).

Answer:

(-10)