1. ## Piecewise snowstorm

Hey everyone, i have this problem:
During a 9 hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate of 2 inches per hour for the next 6, and at a rate of 0.5 per hour for the final hour. Write and graph a piecewise-defined function that gives the depth of the snow during the snowstorm. How many inches of snow accumulated from the storm?

and so i have gotten to this point so far

F(x)= 0, if x <0
= [[x]], if x >0 and x < 2
= 2[[x]]-2, if x => 2 and x <8

and i can not figure out the equation for the 4th part of the function, also would like to know if i am on the right track, any help would be much appreciated, thanks!

2. Hello, eddieg0304!

During a 9 hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours,
at 2 inches per hour for the next 6 hours, and at a rate of 0.5 per hour for the final hour.

Write and graph a piecewise-defined function that gives the depth of the snow during the snowstorm.
How many inches of snow accumulated from the storm?
I sketched the graph first . . .
Code:
        |
|               R
14½+               o
|         Q  *  :
14 +         o     :
|        *:     :
|       * :     :
|      *  :     :
|     *   :     :
|  P *    :     :
2 +   o     :     :
| * :     :     :
- - o - + - - + - - + - -
|   2     8     9
|

First 2 hours: 1 inch per hour.
. . Point $P\!:\;(2,2)$

Next 6 hours: 2 inches per hour.
. . From $t=2$ to $t=8$, 12 inches of snow were added.
. . Pont $Q\!:\;(8,14)$

Last hour: ½ inch per hour.
. . From $t = 8$ to $t = 9,\;\tfrac{1}{2}$ inch was added.
. . Point $R\!:\;(9,14.5)$

$f(x) \;=\;\begin{Bmatrix}x && 0 \leq x < 2 \\ \\[-3mm]2x+2 && 2 \leq x < 8 \\ \\[-3mm] \frac{1}{2}x + 14 && 8 \leq x \leq 9 \end{Bmatrix}$

3. ok now i have a few questions.

$f(x) \;=\;\begin{Bmatrix}x && 0 \leq x < 2 \\
\\[-3mm]2x+2 && 2 \leq x < 8 \\ \\[-3mm] \frac{1}{2}x + 14
&& 8 \leq x \leq 9 \end{Bmatrix}
$

This function is it supposed to be that of the graph? cause if so would you be able to explain how so? i was just doing some checking on it and it didn't seem to pan out, but i am not a 100% sure as my calculator is sort of out of commission right now so i just did it all in my head since they are fairly simple equations, and most definitely thank you for even checking this out and giving me a helping hand

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