In mathematics, a function is a relationship between two sets of values where each input (or independent variable) is associated with exactly one output (or dependent variable). In simpler terms, for every value from the first set (the domain), there is one and only one corresponding value from the second set (the range).
Now, looking at the table you've provided, we can analyze whether it represents a function. The "Day of the Week" serves as the input (independent variable), and the "Number of Children in the Car" serves as the output (dependent variable).
Evaluating the table:
- Sunday has 2 children
- Monday has 4 children
- Tuesday has 4 children
- Wednesday has 3 children
- Thursday has 4 children
- Friday has 3 children
- Saturday has 0 children
In this case, every day of the week (input) corresponds to one specific number of children (output). There are no days that share the same input while producing different outputs. Therefore, since each day has a unique output associated with it, the relationship in the table meets the criteria for a function.
Thus, we can say that this table shows a function because for every day of the week, there is a single and defined number of children in the car, ensuring that each input has one and only one output.
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