The correct answer is option B: the domain is all integers, and the range is all integers that are multiples of 3.
A step function is a piecewise constant function that has only a finite number of pieces. It is defined by dividing the domain into intervals and assigning a constant value to each interval.
In this case, the step function is not explicitly given, but we can infer its properties from the answer choices.
Option A is incorrect because the domain cannot be all real numbers since a step function is a piecewise constant function. Option C is incorrect because the range cannot be all integers that are multiples of 3 since the function may take on other values.
Option D is incorrect because the domain cannot be all integers since the function may be defined on non-integer values.
Therefore, the correct answer is option B, which states that the domain is all integers, and the range is all integers that are multiples of 3.
Complete question:
What are the domain and range of the step function with the equation below?
a. the domain is all real numbers, and the range is all real numbers.
b. the domain is all integers, and the range is all integers that are multiples of 3.
c. the domain is all real numbers, and the range is all integers that are multiples of 3.
d. the domain is all integers, and the range is all real numbers.