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

Answer:

To find the average rate of change of the function (y = f(x)) on the interval ([a,b]=[-2,-1]), we use the formula (\frac{f(b)-f(a)}{b - a}).

First, we need to find (f(-2)) and (f(-1)) from the graph.

• Looking at the graph, when (x=-2), (y = f(-2)= - 20)
• When (x=-1), (y=f(-1)=0)

Now we calculate the average rate of change: [ \begin{align*} \frac{f(-1)-f(-2)}{-1-(-2)}&=\frac{0 - (-20)}{-1 + 2}\ &=\frac{0+20}{1}\ &=20 \end{align*} ] The average rate of change of the function (f(x)) on the interval ([-2,-1]) is (20)

Explanation:

Step1: Identify the formula

The formula for average rate of change is (\frac{f(b)-f(a)}{b - a}) where ([a,b]) is the interval. Here (a=-2) and (b = - 1)

Step2: Find function - values

From the graph, (f(-2)=-20) and (f(-1)=0)

Step3: Substitute values into formula

Substitute (f(-2)=-20), (f(-1)=0), (a=-2) and (b=-1) into (\frac{f(b)-f(a)}{b - a}), we get (\frac{0-(-20)}{-1-(-2)}=\frac{20}{1}=20)