topic #4: general review (not on quiz) 18. what is the average rate of change from x = -2 and x = 0? 19…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$.

Step2: Find $y$ - values for $x=-2$ and $x = 0$ from the graph

From the graph, when $x=-2$, $y = 0$; when $x = 0$, $y=2$.

Step3: Calculate average rate of change for $x=-2$ to $x = 0$

$\frac{f(0)-f(-2)}{0-(-2)}=\frac{2 - 0}{2}=1$.

Step4: Find $y$ - values for $x = 1$ and $x = 2$ from the graph

From the graph, when $x = 1$, $y=0$; when $x = 2$, $y=-2$.

Step5: Calculate average rate of change for $x = 1$ to $x = 2$

$\frac{f(2)-f(1)}{2 - 1}=\frac{-2-0}{1}=-2$.

Answer:

18. 1
19. -2