Question

what are the domain and range of the step function with the equation below?
$f(x)=-3\lceil x \
ceil$

• the domain is all real numbers, and the range is all real numbers.
• the domain is all integers, and the range is all integers that are multiples of 3.
• the domain is all real numbers, and the range is all integers that are multiples of 3.
• the domain is all integers, and the range is all real numbers.

Explanation:

Step1: Identify the domain

The function $f(x) = -3\lceil x
ceil$ uses the ceiling function, which accepts any real number input $x$. So the domain is all real numbers.

Step2: Identify the range

The ceiling function $\lceil x
ceil$ outputs only integers. Multiplying an integer by $-3$ results in integers that are multiples of 3. So the range is all integers that are multiples of 3.

Answer:

The domain is all real numbers, and the range is all integers that are multiples of 3.