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Use the table to answer the question.

.
Day of the Week Number of Children in the Car
Sunday 2
Monday 4
Tuesday 4
Wednesday 3
Thursday 4
Friday 3
Saturday 0
Describe the meaning of the word function in math. Then consider the table. Why does this table show a function?

(2 points)

3 answers

In mathematics, a function is a relation that uniquely associates each element in a set (the domain) with exactly one element in another set (the codomain). In simpler terms, for every input, there is one and only one output.

Considering the provided table, it shows a function because each day of the week (input) corresponds to a specific and unique number of children in the car (output). No day of the week has the same number of children as another day, and every day listed in the table has a defined number of children associated with it. Thus, the relationship between the days of the week and the number of children in the car meets the definition of a function.

but monday tuesday have the same number of children

You are correct; both Monday and Tuesday have the same number of children (4). I apologize for the oversight in my explanation.

In light of that, let's clarify why this table does not represent a function based on the mathematical definition:

A function requires that each input (in this case, each day of the week) is associated with exactly one output (the number of children). While it is acceptable for multiple inputs to share the same output (i.e., both Monday and Tuesday can each have 4 children), the key point is that each individual input has a unique output.

In this case, the table shows that for each specific day of the week, there is only one number associated with it, even if two different days share that same output. Since each day in the table is paired with a single value (the number of children), we can still consider this a function, but it does have some outputs that are shared among different inputs.

In summary, the function aspect of the table holds because each day maps to a single, unique number of children, even if some of those numbers are the same across different days. Thank you for your patience, and I appreciate your attention to detail!