Question

A ball is dropped from the top of a building that is 1,000 feet high. Its height, in feet, as a function of the time, x, in seconds, after the ball was dropped, is given by the following equation, ƒ(x) = 1,000 - 16x 2. Which set of numbers is appropriate as the domain for this function?

Natural Numbers
Positive Real Numbers
Positive Integers
Positive Rational Numbers

Answer 1

Positive real numbers

Explanation:

The domain is all the possible values of x. Here, x represents the time that the ball falls.

Natural numbers are integers greater than 0 (1, 2, 3, etc.). However, the time doesn't have to be an integer (for example, x=1.5).

Positive integers are the same as natural numbers.

Positive rational numbers are numbers greater than 0 that can be written as a ratio of integers (1/1, 3/2, 2/1, etc.). However, the time can also be irrational (for example, x=√2).

Positive real numbers are numbers greater than 0 and not imaginary (don't contain √-1). This is the correct domain of the function.