A mapping diagram is a visual way to represent a function. It shows how each element in the domain (input set) is paired with an element in the range (output set). When determining if a mapping diagram represents a function, we need to check that each input maps to exactly one output. Here's a guide on how to use mapping diagrams to identify functions:
1. Set Up the Mapping Diagram
- Draw two ovals or columns side-by-side.
- Label the first oval as the domain (input values).
- Label the second oval as the range (output values).
- Write each input value in the domain oval and each output value in the range oval.
2. Draw Arrows for Mapping
- Draw an arrow from each input value in the domain to its corresponding output value in the range.
- Each arrow represents the relationship or pairing between an input and an output.
3. Apply the Definition of a Function
In mathematical terms, a function is a relationship where each input has exactly one output. To determine if the mapping diagram is a function:
- Check each input value in the domain.
- Each input should have one and only one arrow pointing to an output.
- It is not a function if an input has more than one arrow pointing to different outputs.
- If each input has exactly one arrow, then it represents a function.
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