Consider the following function definition.Domain: The set of months {January, February, ..., December}.Codomain: All integers in the range [1, 31].Rule: f(month) = number of days in that month in 2025Which of these statements is true with respect to this function?

Question

BlackTom AI · Accepted Answer

Firstly, recall the setup: the domain is the 12 months, the codomain is the set of integers from 1 to 31, and f(month) returns the number of days in that month for the year 2025. Since 2025 is not a leap year, February has 28 days. January, March, May, July, August, October, and December each have 31 days, while April, June, September, and November have 30 days. This means the image of f is the set {28, 30, 31}.

Option a. 'The image is a proper subset of the codomain.' This statement is true because every value in the image (28, 30, 31) lies within the codomain {1, 2, ..., 31}, so the image is a subset of the codomain. Moreover, the image does not contain every element of the codomain; for example, 1, 2, ..., 27, 29, and others are not attained by f. Therefore, it is not equal to the entire codomain, which makes it a proper subset.

To see why the image is not the whole codomain, notice that the codomain includes many integers that never occur as the number of days in any month (such as 1 or 2 days, or 7 days, etc.), and f(month) only yields 28, 30, or 31 for this particular year. Hence, the claim that the image is a proper subset is accurate.

If we were to evaluate other possibilities (even though they aren’t listed), we would find statements like 'the image equals the codomain' would be false since 1–27 and 29–31 are not all attained, and 'the image is not a subset' would be false since all image values are contained in the codomain. The core idea is: the image sits inside the codomain, but does not cover it completely, confirming the proper-subset relationship.

Consider the following function definition.Domain: The set of months {January, February, ..., December}.Codomain: All integers in the range [1, 31].Rule: f(month) = number of days in that month in 2025Which of these statements is true with respect to this function?

查看解析

登录即可查看完整答案

类似问题

Which of the following set of ordered pairs does not represent a function?

Consider the function f:R→R, with the rule f(x). Which of the following would be a valid choice for the rule f(x)?

Question textWhich type of relation is presented in the graph below?[select: (Clear my choice), one to one, many to one, many to many, one to many] Your last answer was interpreted as follows: [math: many to one] \mbox{many to one}

Which of the following relations is not a function? (K:1)

Consider the following function definition:Domain: The set of negative integers Codomain: The set of integers Rule: f(x) = x + 7 Which of the following would be an ordered pair belonging to this function?

What would be the best description of the rule for this function?

Which of the following statements is true about functions?

The variable is a complex function that depends on which of the following?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单