Section 4.7: Relations & Mapping
A relation is a set of ordered pairs, and a mapping diagram visually represents how each element of the domain corresponds to an element in the range.
Example 1
Given the relation \( \{(1,2), (3,4), (5,6)\} \), create a mapping diagram.
Draw two columns: domain {1,3,5} and range {2,4,6}, then connect 1→2, 3→4, 5→6.
Example 2
Determine if the relation \( \{(2,3), (4,3), (6,5)\} \) is a function.
Yes, each input (2, 4, 6) maps to exactly one output. Thus it is a function.
Practice Problems
- Draw a mapping diagram for \( \{(a,1), (b,2), (c,1)\} \).
- Identify whether the relation \( \{(1,2),(2,2),(3,2),(1,3)\} \) is a function.
- Create a table for the function \( f(x) = x+1 \) for \( x = 0,1,2,3 \).
- Given a mapping diagram, list all ordered pairs.
- Explain why a function cannot have one input mapping to multiple outputs.