Integrated Math 1 / Unit 3: Functions
3.1 Relations and Functions
Notes
A relation pairs inputs with outputs. A function is a relation in which each input has exactly one output.
- Check ordered pairs: no $x$-value may repeat with different $y$-values. Repeated outputs are fine.
- Vertical line test: a graph is a function if no vertical line crosses it more than once.
- Example: $\{(1, 4), (2, 4), (3, 7)\}$ is a function; $\{(1, 4), (1, 5)\}$ is not.
- Functions can be shown as tables, graphs, equations, mappings or words.
Practice
Which set of ordered pairs is a function?
In the second set every input (2, 3, 4) has exactly one output. Repeated outputs are allowed.
What does the vertical line test check?
If a vertical line hits the graph twice, one input has two outputs.
Which relationship is NOT a function?
The input 9 has two outputs, 3 and $-3$, so it fails the one-output rule.
Ready for more? Take the Unit 3 test.