To determine whether each relation represents a function, we need to check if each element in the domain (input) is mapped to exactly one element in the range (output). A relation is a function if and only if no input value is associated with more than one output value.
Let's analyze each diagram step by step:
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Diagram 1:
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Domain: {0, 2, 4, 6}
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Range: {–2, –1, 0, 1, 2}
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Mapping:
- 0 → –2
- 2 → 0
- 4 → 1
- 6 → 2
Each input value is mapped to exactly one output value. Therefore, this relation is a function.
Answer for Diagram 1: Function
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Diagram 2:
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Domain: {–14, –13, –12, –11, –10}
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Range: {–5, –4, –3, –2, –1, 0}
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Mapping:
- –14 → –5
- –13 → –4
- –12 → –3
- –11 → –2
- –10 → –1
Each input value is mapped to exactly one output value. Therefore, this relation is a function.
Answer for Diagram 2: Function
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Diagram 3:
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Domain: {–2, –1, 0, 1, 2, 3}
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Range: {–10, –8, –6, –4, –2, 0, 2, 4, 6, 8, 10}
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Mapping:
- –2 → –10
- –1 → –8
- 0 → –6
- 1 → –4
- 2 → –2
- 3 → 0
Each input value is mapped to exactly one output value. Therefore, this relation is a function.
Answer for Diagram 3: Function
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Diagram 4:
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Domain: {1, 2, 3, 4, 5, 6}
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Range: {–1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
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Mapping:
- 1 → 0
- 2 → 2
- 3 → 4
- 4 → 6
- 5 → 8
- 6 → 10
Each input value is mapped to exactly one output value. Therefore, this relation is a function.
Answer for Diagram 4: Function
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Diagram 5:
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Domain: {–10, –8, –6, –4, –2, 0, 2, 4, 6, 8, 10}
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Range: {–20, –16, –12, –8, –4, 0, 4, 8, 12, 16, 20}
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Mapping:
- –10 → –20
- –8 → –16
- –6 → –12
- –4 → –8
- –2 → –4
- 0 → 0
- 2 → 4
- 4 → 8
- 6 → 12
- 8 → 16
- 10 → 20
Each input value is mapped to exactly one output value. Therefore, this relation is a function.
Answer for Diagram 5: Function
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Diagram 6:
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Domain: {–3, –2, –1, 0, 1, 2, 3, 4, 5, 6}
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Range: {–15, –10, –5, 0, 5, 10, 15, 20}
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Mapping:
- –3 → –15
- –2 → –10
- –1 → –5
- 0 → 0
- 1 → 5
- 2 → 10
- 3 → 15
- 4 → 20
- 5 → 15
- 6 → 10
Here, the input values 5 and 6 are both mapped to multiple output values (5 → 15 and 6 → 10). This violates the definition of a function, as an input cannot be associated with more than one output.
Answer for Diagram 6: Not a Function
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Final Answers:
1. Function
2. Function
3. Function
4. Function
5. Function
6. Not a Function
Boxed Answer:
\[
\boxed{\text{Function, Function, Function, Function, Function, Not a Function}}
\]
Parent Tip: Review the logic above to help your child master the concept of function mapping worksheet.
