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 $-4 \\leq x \\leq 0$?

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-4 \\leq x \\leq 0$?

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=-4 ) and ( b = 0 ).

Step2: Find ( f(-4) ) and ( f(0) ) from the graph

From the graph, when ( x=-4 ), the ( y )-value (i.e., ( f(-4) )) is ( 0 ) (since the graph passes through ((-4, 0))). When ( x = 0 ), the ( y )-value (i.e., ( f(0) )) is ( -8 ) (since the graph passes through ((0, -8))).

Step3: Substitute into the formula

Substitute ( a=-4 ), ( b = 0 ), ( f(-4)=0 ), and ( f(0)=-8 ) into the average rate of change formula: [ \frac{f(0)-f(-4)}{0 - (-4)}=\frac{-8 - 0}{0 + 4}=\frac{-8}{4}=-2 ]

Answer:

(-2)