Exercises

For each of the relationships in Exercises 1 – 16, determine whether the relation is or is not a function. If the relation is a function, is it a function of time?

1. The height of a baseball after being hit into the air.
2. The speed of an egg dropped from the tenth floor of a building.
3. The height of an individual as he or she ages.
4. The amount of time it takes a person to run a mile as he or she ages.
5. The amount of money in a savings account over an extended period of time.
6. The size of a person's vocabulary from birth onwards.
7. The number of bacteria in a laboratory culture over a period of time.
8. The daily high temperature at your local airport over a calendar year.
9. The number of students absent from class and the day of the academic year.
10. The temperature of an ice-cold drink left in a warm room over a period of time.
11. The number of hours of daylight and the day of the year.
12. The cost of a pizza and the diameter of the pizza.
13. A safe following distance for your car at a given speed.
14. Ideal weight at a given height, as represented by a chart in your doctor's office.
15. The income tax on a given taxable income.
16. The sales tax on a given purchase.
17. Some thermometers measure temperatures on both Fahrenheit and Celsius scales. These side-by-side scales suggest a functional relationship.

    1. Define Fahrenheit temperature as a function of Celsius temperature by a simple formula.
    2. Now express Celsius temperature as a function of Fahrenheit temperature.
    3. What temperature is assigned the same number on both the Fahrenheit and Celsius scales?
       

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