When comparing prices for activities at a local recreation center, you notice that the center charges different prices on different days of the week. For example, riding a go-kart costs $10 on Saturday and Sunday and $5 on Monday through Friday.

Question

Is the cost a function of the activity type? Explain why or why not.

Answer 1

The cost of riding a go-kart is not a function of the activity type alone when considering the information given. In mathematical terms, a function relates each input to exactly one output. In this scenario, the type of activity (riding a go-kart) can lead to different outputs (prices) depending on the day of the week.

For example:

• If you consider the input as the activity type (riding a go-kart), the output (price) changes based on the day:
  • On Saturday and Sunday, the output price is $10.
  • On Monday through Friday, the output price is $5.

Since a single input (the activity type) can produce multiple outputs (the price varies by day), we can conclude that the cost is not a function of just the activity type; it is a function of both the activity type and the day of the week.