4.1 Relations and Functions
Notes
A relation pairs inputs with outputs. A function is a relation where every input has exactly one output.
- The domain is the set of inputs ($x$-values). The range is the set of outputs ($y$-values).
- Vertical line test: a graph is a function if no vertical line crosses it more than once.
- In a table or list of ordered pairs, a repeated $x$ with different $y$-values means it is not a function.
Practice
Which set of ordered pairs is a function?
Each input appears once. Repeated outputs are fine.
What is the domain of $(-2, 4), (0, 1), (3, 4), (5, -1)$?
The domain is the set of $x$-values.
A circle drawn on a coordinate grid is not a function because:
It fails the vertical line test.
Ready for more? Take the Unit 4 test.