Jim says that the output of the floor function is the number before the decimal point in the input. For what domain is Jim’s statement correct? Justify your answer.

  integers ∪ [0, ∞)

Step-by-step explanation:

The floor function gives the largest integer not greater than the input value. For non-negative numbers, that is the integer portion of the number, as Jim says.

However, for negative numbers, the floor is one less than the integer portion of any number that has a non-zero fractional part.

  floor(1.2) = 1

  floor(0.2) = 0

  floor(-0.2) = -1

  floor(-1.2) = -2

For any integer, negative or otherwise, the floor function gives that integer value.

Jim is correct on the domain of all integers and positive non-integers.