Mapping Diagrams – Arrows from Input to Output
A mapping diagram shows a function visually: one column lists the inputs, another lists the outputs, and an arrow is drawn from each input to the output it matches – a direct picture of the function-machine idea you've already met. Mapping diagrams make one crucial rule about functions immediately visible: every input must have exactly one arrow leaving it.
This one-arrow-per-input rule is the actual definition of what makes a relationship a function at all – if a single input had two arrows going to two different outputs, the relationship wouldn't qualify as a function. Mapping diagrams are one of the fastest ways to test this rule at a glance.
Reading and Testing a Mapping Diagram
A mapping diagram is a valid function only if every input has exactly one arrow leaving it. An input with two different outputs is not a function.
The input 2 has two arrows, going to both 5 and 9: no, this is not a valid function.
Real-Life Application
- Vending machines: each button (input) must lead to exactly one snack (output) to work correctly.
- Assigning seat numbers: each ticket (input) should map to exactly one seat (output).
- Postal codes: each address maps to exactly one postal code, a real-world function.
Key Takeaways
- A mapping diagram shows arrows connecting each input to its output.
- A valid function has exactly one arrow leaving every input.
- An input with two different outputs breaks the definition of a function.
Practice: Mapping Diagrams
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