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The Parking Lot

Alignments to Content Standards: F-IF.A.1


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.

  1. Complete the table below.

    $t$ (minutes) $C(t)$ (dollars)
  2. Sketch a graph of $C$ for $0 \leq t \leq 480$.
  3. Is $C$ a function of $t$? Explain your reasoning.
  4. 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 real-world 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.


  1. $t$ (minutes) $C(t)$ (dollars)
    0 0
    $15$ $0.50$
    $20$ $0.50$
    $35$ $1.00$
    $75$ $1.50$
    $125$ $2.50$
    As a sample calculation, we note that $125$ minutes is two full hours (four half-hours) and part of another half hour. Since the ticketing scheme rounds up to the nearest half-hour, we have to pay for five half-hours, at a total cost of \$2.50.
  2. Redone_parking_lot_b8361c7ad2f974944824d6f4cb058dca
  3. Yes, $C$ is a function of $t$ because for a given parking time of $t$ minutes there is exactly one charge.
  4. 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.