Question

Samantha works at an animal shelter. She decides to track the total number of kittens that are brought in. The

equation k = 4w + 3 represents the total number of kittens, where w represents the number of weeks that have
passed since she started counting.
Which statement correctly analyzes the domain of this situation?

A)The domain represents the total number of kittens that came into the shelter. The domain is all real numbers.

B)The domain represents the total number of kittens that have come into the shelter. The domain is all whole numbers.

C)The domain represents the weeks that have passed since Samantha started counting the kittens. The domain is all whole numbers.

D)The domain represents the weeks that have passed since Samantha started counting the kittens.The domain is all real numbers​

Answer 1

C) The domain represents the weeks that have passed since Samantha started counting the kittens. The domain is all whole numbers.

Explanation:

The problem statement tells you the independent variable w represents weeks that have passed. "Domain" refers to values the independent variable may have, so choices A or B make no sense here.

Time is measured continuously, and fractions of a week are possible. So, the domain could be non-negative real numbers. However, the answer choice D is "all real numbers", which includes negative numbers for which the function makes no sense.

The domain "all whole numbers" includes non-negative integers. It is reasonable to restrict the domain to non-negative integer numbers of weeks, so answer choice C is the best option.