Question

Let f be the ceiling function above. Let us determine f(2), f(2.1), f(2.9), f(−2.9).

A) 2, 3, 3, -2
B) 2, 3, 3, -3
C) 2, 3, 3, -4
D) 2, 3, 3, -1

Answer 1

The ceiling function rounds up to the nearest integer. The values for f(2), f(2.1), f(2.9), and f(−2.9) using the ceiling function are 2, 3, 3, and -2 respectively. Hence, the correct answer is A) 2, 3, 3, -2.

Step-by-step explanation:

The student asked about the values of the ceiling function for several numbers: f(2), f(2.1), f(2.9), and f(−2.9). The ceiling function, denoted as ⌈x⌉, rounds the input x up to the smallest integer greater than or equal to x. Using this definition:

1. f(2) = 2 because 2 is already an integer.
2. f(2.1) = 3 because the next integer greater than 2.1 is 3.
3. f(2.9) = 3 similarly because the next integer greater than 2.9 is also 3.
4. f(−2.9) = −2 because when dealing with negative numbers, the ceiling function still rounds up, which means moving towards zero. Hence, it goes from −2.9 to −2.

Therefore, the correct answer to the question is A) 2, 3, 3, -2.