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 $-5 \\leq x \\leq 0$?

the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-5 \\leq x \\leq 0$?

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=-5 ) and ( b = 0 ), so we need to find ( f(-5) ) and ( f(0) ).

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

Looking at the graph, when ( x=-5 ), we observe the ( y )-value (the value of ( f(-5) )). From the graph, at ( x = - 5 ), the point is on the curve, and we can see that ( f(-5)=4 ) (by looking at the y - coordinate of the point corresponding to ( x=-5 )).

Step3: Find ( f(0) ) from the graph

When ( x = 0 ), looking at the graph, the ( y )-value ( ( f(0) )) is ( - 10 ) (from the y - axis intersection point or the point on the graph at ( x = 0 )).

Step4: Calculate the average rate of change

Using the formula (\frac{f(b)-f(a)}{b - a}), substitute ( a=-5 ), ( b = 0 ), ( f(a)=f(-5) = 4 ) and ( f(b)=f(0)=-10 ).

So, (\frac{f(0)-f(-5)}{0-(-5)}=\frac{-10 - 4}{0 + 5}=\frac{-14}{5}=-2.8)

Answer:

(-\frac{14}{5}) (or (-2.8))