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 $-5 \\leq x \\leq -4$?

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-5 \\leq x \\leq -4$?

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=-5 ) and ( b = - 4 ).

Step2: Find ( f(-5) ) and ( f(-4) ) from the graph

From the graph, we can see that when ( x=-5 ), the ( y )-value (i.e., ( f(-5) )) is (-2) (since the point is at ((-5, - 2))), and when ( x = - 4 ), the ( y )-value (i.e., ( f(-4) )) is (-4) (since the point is at ((-4, - 4))).

Step3: Substitute into the formula

Substitute ( a=-5 ), ( b = - 4 ), ( f(-5)=-2 ) and ( f(-4)=-4 ) into the formula (\frac{f(b)-f(a)}{b - a}). We get (\frac{f(-4)-f(-5)}{-4-(-5)}=\frac{-4-(-2)}{-4 + 5}=\frac{-4 + 2}{1}=\frac{-2}{1}=-2).

Answer:

(-2)