Question

Consider a function that describes how a particular car’s gas mileage depends on its speed. What would be an appropriate domain for this function?

0 to 100 miles per hour
0 to 50 miles per gallon
times from 0 to 10 minutes
times from –10 to 10 minutes

Answer 1

To determine an appropriate domain for the function that describes how a car’s gas mileage depends on its speed, we should consider the range of speeds at which a car typically operates.

Here are the provided options:

1. **0 to 100 miles per hour**: This makes sense as a domain because it encompasses the range of speeds at which most cars operate. Speeds of 0 mph (the car is stationary) up to 100 mph (a high, but not unreasonable, driving speed) are realistic values to consider for a car's speed.

2. **0 to 50 miles per gallon**: This does not make sense as a domain for the speed function because "miles per gallon" is a measure of fuel efficiency, not speed.

3. **Times from 0 to 10 minutes**: This does not make sense because the domain should represent speeds, not times.

4. **Times from –10 to 10 minutes**: This is also inappropriate as it involves both times and negative values, which do not relate to the car's speed in a meaningful way for this context.

Thus, the most appropriate domain for a function describing how a car’s gas mileage depends on its speed is:

**0 to 100 miles per hour.**