In mathematics, a function is a relation where every input has a unique output. Let's analyze each pairing to determine which one describes a function:
1. (number of doors in a car, number of cup holders in the car):
- Different cars with the same number of doors can have a different number of cup holders. For example, two different cars both with 4 doors might have 6 and 7 cup holders, respectively.
- Not a function because a single input (number of doors) can correspond to multiple outputs (numbers of cup holders).
2. (height of a building in feet, height of the building in inches):
- The height of a building in feet determines exactly one height in inches because there is a specific conversion factor (1 foot = 12 inches).
- Is a function because each input (height in feet) has exactly one unique output (height in inches).
3. (beverage charge on a bill, total meal charge on the bill):
- The total meal charge includes not only the beverage charge but also the cost of food, tax, tips, etc. If you know only the beverage charge, you cannot uniquely determine the total meal charge.
- Not a function because a single input (beverage charge) can correspond to multiple outputs (total meal charges).
4. (distance from home during a trip, time elapsed during the trip):
- The distance from home can vary with different routes taken and stops made, even for the same amount of time elapsed. Two trips of the same duration might cover different distances.
- Not a function because a single input (time elapsed) can correspond to multiple outputs (distances from home).
Among the given options, the only pairing that describes a function is:
- (height of a building in feet, height of the building in inches)
This pairing always maps each input (height of a building in feet) to a unique output (height of the building in inches).
