Solved Examples of Mapping Diagrams for Relations and Functions

📚 Quick Study Guide

• 🗺️ A mapping diagram visually represents a relation or function using arrows to connect elements from the domain to the range.
• 🎯 The domain is the set of all possible input values (often called 'x' values).
• 📈 The range is the set of all possible output values (often called 'y' values).
• 🔗 In a function, each element in the domain maps to exactly one element in the range.
• 🚫 If any element in the domain maps to more than one element in the range, the relation is NOT a function.
• ✍️ Mapping diagrams help determine if a relation is a function by checking for one-to-one or many-to-one mappings, but not one-to-many.
• 🧮 Example: If the domain is $A = \{1, 2, 3\}$ and the range is $B = \{4, 5, 6\}$, a mapping could show 1 → 4, 2 → 5, and 3 → 6.

🧪 Practice Quiz

1. Question 1: Which of the following mapping diagrams represents a function?
   1. A: A maps to both X and Y, B maps to Z
   2. B: A maps to X, B maps to Y, C maps to Z
   3. C: A maps to X, A maps to Y, B maps to Z
   4. D: A maps to X, B maps to X, C maps to X
2. Question 2: In a mapping diagram, if one element in the domain maps to two different elements in the range, what does this indicate?
   1. A: It is a function.
   2. B: It is not a function.
   3. C: It is a one-to-one function.
   4. D: It is a linear function.
3. Question 3: Given the relation {(1, a), (2, b), (3, c), (1, d)}, which mapping diagram represents this relation?
   1. A: 1→a, 2→b, 3→c
   2. B: 1→a, 2→b, 3→c, 1→d
   3. C: 1→a, 2→b, 3→c, d→1
   4. D: a→1, b→2, c→3, d→1
4. Question 4: Which of the following sets of ordered pairs represents a function?
   1. A: {(1, 2), (2, 3), (3, 4), (1, 5)}
   2. B: {(1, 2), (2, 2), (3, 2), (4, 2)}
   3. C: {(1, 2), (1, 3), (1, 4), (1, 5)}
   4. D: {(1, 2), (2, 3), (3, 2), (2, 1)}
5. Question 5: What is the domain of the relation represented by the mapping diagram: A→X, B→Y, C→Z?
   1. A: {X, Y, Z}
   2. B: {A, B, C, X, Y, Z}
   3. C: {A, B, C}
   4. D: {1, 2, 3}
6. Question 6: What is the range of the relation represented by the mapping diagram: 1→a, 2→a, 3→b?
   1. A: {1, 2, 3}
   2. B: {a, b}
   3. C: {1, 2, 3, a, b}
   4. D: {a, a, b}
7. Question 7: Which mapping diagram represents a one-to-one function?
   1. A: A→X, B→X, C→X
   2. B: A→X, B→Y, C→X
   3. C: A→X, B→Y, C→Z
   4. D: A→X, A→Y, B→Z