Answer:
a. -2 b. -2 c. -1 d. 4 e. -3 f. 0
Step-by-step explanation:
The average rate of change formula is:
[tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]
a.
We need to find the rate of change for x = -3 to x = -2 so we look on the graph to find y.
At x = -3 it look like y = 0 so
[tex]x_{1} = -3[/tex]
[tex]y_{1} = 0[/tex]
At x = -2 it looks like y = 2
[tex]x_{2} = -2[/tex]
[tex]y_{2} = 2[/tex]
Now we can just plug everything in to the rate of change formula.
[tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}} = \frac{2- 0}{-3-(-2)} = \frac{2- 0}{-3+2} = \frac{2}{-1}[/tex] = -2
So for a. our rate of chage for the given interval is -2
b.
Now that you have the formula we don't need to explain each time.
[tex]x_{1} =[/tex] -2
[tex]y_{1} =[/tex] 2
[tex]x_{2} =[/tex] 1
[tex]y_{2} =[/tex] - 4
[tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}} = \frac{-4- 2}{1-(-2)} = \frac{-4-2}{1+2} = \frac{-6}{3}[/tex] = -2
c.
[tex]x_{1} =[/tex] 0
[tex]y_{1} =[/tex] -3
[tex]x_{2} =[/tex] 1
[tex]y_{2} =[/tex] - 4
[tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}} = \frac{-4-(-3)}{1-0} = \frac{-4 + 3}{1-0} = \frac{-1}{1}[/tex] = -1
d.
[tex]x_{1} =[/tex] 1
[tex]y_{1} =[/tex] -4
[tex]x_{2} =[/tex] 2
[tex]y_{2} =[/tex] 0
[tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}} = \frac{0 - (-4)}{2-1} = \frac{0 + 4}{2-1} = \frac{4}{1}[/tex] = 4
e.
[tex]x_{1} =[/tex] -1
[tex]y_{1} =[/tex] 0
[tex]x_{2} =[/tex] 0
[tex]y_{2} =[/tex] -3
[tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}} = \frac{-3- 0}{0-(-1)} = \frac{-3- 0}{0+1} = \frac{-3}{1}[/tex] = -3
f.
[tex]x_{1} =[/tex] -1
[tex]y_{1} =[/tex] 0
[tex]x_{2} =[/tex] 2
[tex]y_{2} =[/tex] 0
[tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}} = \frac{0- 0}{2-(-1)} = \frac{0- 0}{2+1} = \frac{0}{3}[/tex] = 0
