In mathematics, a function is a specific kind of relation between a set of inputs and a set of possible outputs. For each input from the domain, a function assigns exactly one output from the codomain. This means that no two distinct inputs can produce the same output; in other words, each input must correspond to one and only one output.
For example, if we define a function \( f \) that assigns the number of kids in a car based on the day of the week, we can think of the days (Sunday through Saturday) as inputs, and the number of kids as outputs.
Now, regarding the table you provided:
- Sunday: 2 kids in car
- Monday: 4 kids in car
- Tuesday: 4 kids in car
- Wednesday: 3 kids in car
- Thursday: 4 kids in car
- Friday: 3 kids in car
- Saturday: 0 kids in car
To determine if this table represents a function, we need to evaluate whether each input (day of the week) corresponds to exactly one output (number of kids in the car).
In this case, we can see that each day of the week is listed only once, and while multiple days may have the same output (e.g., Monday, Tuesday, and Thursday all have 4 kids), each specific day leads to only one specific number of kids. Therefore, the table meets the criteria for being a function.
In summary, the table shows a function because:
- Each day of the week (input) is unique and corresponds to one specific number of kids (output).
- No day is associated with more than one output, consistent with the definition of a function.
1 answer