Question

Let f be the floor function, and find f(2), f(2.1), f(2.9), f(−2.1), and f(π).

A) 2, 2, 2, -3, 3
B) 2, 2, 3, -2, 3
C) 2, 3, 3, -3, 3
D) 2, 2, 2, -2, 3

Answer 1

The floor function rounds down to the nearest whole number. For the given values, it results in f(2) = 2, f(2.1) = 2, f(2.9) = 2, f(-2.1) = -2, f(π) = 3. Therefore, Option B is the correct answer.

Step-by-step explanation:

The floor function, denoted as f(x), returns the greatest integer less than or equal to x. In other words, it "rounds down" to the nearest whole number. Here's how it evaluates for each given value:

• f(2) = 2 because 2 is already an integer.
• f(2.1) = 2 because 2 is the greatest integer less than or equal to 2.1.
• f(2.9) = 2 because 2 is still the greatest integer less than or equal to 2.9.
• f(-2.1) = -3 because -3 is the greatest integer less than or equal to -2.1.
• f(π) ≈ f(3.14) = 3 since π is approximately 3.14 and 3 is the greatest integer less than or equal to π.

Comparing these results to the provided options, Option B is correct: f(2) = 2, f(2.1) = 2, f(2.9) = 2, f(-2.1) = -2, f(π) = 3.