The Parking Lot
Alignments to Content Standards:
FIF.A.1
Task
A parking lot charges $\$0.50$ for each half hour or fraction thereof, up to a daily maximum of $\$10.00$. Let $C(t)$ be the cost in dollars of parking for $t$ minutes.

Complete the table below.
$t$ (minutes) $C(t)$ (dollars) 0 $15$ $20$ $35$ $75$ $125$  Sketch a graph of $C$ for $0 \leq t \leq 480$.
 Is $C$ a function of $t$? Explain your reasoning.
 Is $t$ a function of $C$? Explain your reasoning.
IM Commentary
The purpose of this task is to investigate the meaning of the definition of function in a realworld context where the question of whether there is more than one output for a given input arises naturally. In more advanced courses this task could be used to investigate the question of whether a function has an inverse.
Solution

$t$ (minutes) $C(t)$ (dollars) 0 0 $15$ $0.50$ $20$ $0.50$ $35$ $1.00$ $75$ $1.50$ $125$ $2.50$  Yes, $C$ is a function of $t$ because for a given parking time of $t$ minutes there is exactly one charge.
 No, $t$ is not a function of $C$ because there are values of $C$ that have many values of $t$ associated with them. For example if you end up paying $\$0.50$ then you could have parked for any period of time up to half an hour, that is, when $C = 0.50$ then $t$ can have any value in the range $0 < t \le 30$. So the "input" $C = 0.50$ yields more than one output, which is not allowed for a function.
The Parking Lot
A parking lot charges $\$0.50$ for each half hour or fraction thereof, up to a daily maximum of $\$10.00$. Let $C(t)$ be the cost in dollars of parking for $t$ minutes.

Complete the table below.
$t$ (minutes) $C(t)$ (dollars) 0 $15$ $20$ $35$ $75$ $125$  Sketch a graph of $C$ for $0 \leq t \leq 480$.
 Is $C$ a function of $t$? Explain your reasoning.
 Is $t$ a function of $C$? Explain your reasoning.