Question

Select the correct description of the function f: f(x) = ŒˆxŒ‰.

1) The function f rounds up the input x to the nearest integer.
2) The function f rounds down the input x to the nearest integer.
3) The function f returns the absolute value of the input x.
4) The function f returns the ceiling value of the input x.

Answer 1

The function f(x) = ŒˆxŒ‰ is known as the floor function, which rounds down the input x to the nearest integer. The correct answer to the question is option 2.

Step-by-step explanation:

The correct description of the function f: f(x) = ŒˆxŒ‰ is that it rounds down the input x to the nearest integer. This type of function is known as the floor function. When you apply the floor function to any real number, it gives you the greatest integer that is less than or equal to that number. For example, applying f to 3.7 would give 3 since 3 is the largest integer less than or equal to 3.7. Therefore, the answer to the student's question is option 2: The function f rounds down the input x to the nearest integer.