CPM Homework Help : APCALC Problem 2-126

The rate of customers who pass through the checkout stand at a grocery store depends on the time of day. Assume the rate follows the following piecewise-defined function, where $x$ represents the time of day (in hours) after 9:00 a.m. and $f (x)$ is the number of customers served per hour.

$f ( x ) = \left\{ \begin{array} { l l } { 120 x } & { \text { for } 0 \leq x < 2 } \\ { 180 x - 120 } & { \text { for } 2 \leq x < 5 } \\ { 240 x - 420 } & { \text { for } x \geq 5 } \end{array} \right.$

Graph the function and state its domain and range.
Graph (a):
Your sketch should have three linear pieces.
Hint (a):
The domain is given by the piecewise function above.
More Help (a):
The range can be seen on the graph. What is the highest and lowest $y$ -value? Are there any holes or jumps on that interval?
Is this function continuous?
Hint (b):
We know that the graph has a starting point $(0 ,0)$ so, it could only be continuous when $x > 0$ .
More Help (b):
Be mindful of the $3$ conditions of continuity:
Calculate the area under the curve for $0\le x\le8$ . What are the units of this area? What does this area represent?
Hint (c):
$\text{Area = k(base)(height)}$ , where $k$ is some constant. The base is determined by the units on the $x$ -axis. The height is determined by the units on the $y$ -axis. Multiply.