problems 30—32 the graph of function f is shown. write the correct number in each box as a fraction in…

problems 30—32 the graph of function f is shown. write the correct number in each box as a fraction in lowest terms. 30. the average rate of change of f from -7 to 8 is. 31. the average rate of change of f from -2 to 5 is. 32. the average rate of change of f from -4 to 12 is.

problems 30—32 the graph of function f is shown. write the correct number in each box as a fraction in lowest terms. 30. the average rate of change of f from -7 to 8 is. 31. the average rate of change of f from -2 to 5 is. 32. the average rate of change of f from -4 to 12 is.

Answer

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 given by $\frac{f(b)-f(a)}{b - a}$.

Step2: For problem 30

From the graph, assume $f(-7)=y_1$ and $f(8)=y_2$. Count the grid - points to find $f(-7)= - 4$ and $f(8)=3$. Then the average rate of change is $\frac{f(8)-f(-7)}{8-(-7)}=\frac{3-(-4)}{8 + 7}=\frac{3 + 4}{15}=\frac{7}{15}$.

Step3: For problem 31

From the graph, assume $f(-2)=y_3$ and $f(5)=y_4$. Count the grid - points to find $f(-2)=0$ and $f(5)= - 3$. Then the average rate of change is $\frac{f(5)-f(-2)}{5-(-2)}=\frac{-3-0}{5 + 2}=-\frac{3}{7}$.

Step4: For problem 32

From the graph, assume $f(-4)=y_5$ and $f(12)=y_6$. Count the grid - points to find $f(-4)= - 2$ and $f(12)=1$. Then the average rate of change is $\frac{f(12)-f(-4)}{12-(-4)}=\frac{1-(-2)}{12 + 4}=\frac{1 + 2}{16}=\frac{3}{16}$.

Answer:

  1. $\frac{7}{15}$
  2. $-\frac{3}{7}$
  3. $\frac{3}{16}$