In mathematics, a function is a relationship or a rule that assigns each input exactly one output. In simpler terms, for every value in a set called the domain, there is a corresponding value in a set called the range. Essentially, a function takes an input (often referred to as \( x \)) and produces a single output (often referred to as \( y \)).
To determine if a relation is a function, one must check that each input is associated with only one output. If any input corresponds to multiple outputs, then the relation is not a function.
Now, looking at the table provided:
| Day of the Week | Number of Children in the Car | |------------------|-------------------------------| | Sunday | 2 | | Monday | 4 | | Tuesday | 4 | | Wednesday | 3 | | Thursday | 4 | | Friday | 3 | | Saturday | 0 |
This table shows that each day of the week (the input) corresponds to a specific number of children in the car (the output).
- Sunday: 2 children
- Monday: 4 children
- Tuesday: 4 children
- Wednesday: 3 children
- Thursday: 4 children
- Friday: 3 children
- Saturday: 0 children
Each day is unique and does not repeat with different outputs; therefore, there are no days of the week that correspond to more than one number of children. Although some days may share the same number of children (e.g., Monday, Tuesday, and Thursday all show 4 children), each unique input (day of the week) only has one output (number of children).
Thus, this table represents a function because each day of the week as an input has exactly one corresponding output in terms of the number of children in the car.