what is the average rate of change of f over the interval -3,9? give an exact number.

Answer:

To find the average rate of change of a function $y = f(x)$ over the interval $[a,b]$, we use the formula $\frac{f(b)-f(a)}{b - a}$. Here, $a=-3$ and $b = 9$. We need to find the values of $f(-3)$ and $f(9)$ from the graph. Let's assume from the graph that $f(-3)=y_1$ and $f(9)=y_2$. The average rate of change $=\frac{f(9)-f(-3)}{9-(-3)}=\frac{y_2 - y_1}{12}$

Since the graph is not clear - enough to read the exact values of $y_1$ and $y_2$, we'll just state the general formula for the average rate of change. If we could determine from the graph that $f(-3)=m$ and $f(9)=n$, then the average rate of change would be $\frac{n - m}{12}$

Explanation:

Step1: Recall average - rate - of - change formula

The formula for the average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$.

Step2: Identify $a$ and $b$ values

Here, $a=-3$ and $b = 9$, so the denominator is $b - a=9-(-3)=12$.

Step3: Determine $f(a)$ and $f(b)$ values

We need to find $f(-3)$ and $f(9)$ from the graph. Let them be $y_1$ and $y_2$ respectively. Then the average rate of change is $\frac{y_2 - y_1}{12}$.