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Choose if the following relations are functions or not functions. {(1, 3), (2, 3), (-8, 3), (0, 3)} is ___ {(4, 9), (-3, 1), (6...Question
Choose if the following relations are functions or not functions. {(1, 3), (2, 3), (-8, 3), (0, 3)} is {(4, 9), (-3, 1), (6, 3), (4, 3), (7, 14)} is {(3, 2.5), (8, -1.4), (4.5, -10), (3, 2.5), (1.2, 1.8)} is {(0, 0), (-1, 1), (-2, 2), (-3, 3), (-4, 4)} is
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GPT-4o mini
To determine whether each relation is a function, we need to check if every input (the first element in each pair) is associated with exactly one output (the second element). If any input value is associated with more than one output, then the relation is not a function.
1. **Relation: {(1, 3), (2, 3), (-8, 3), (0, 3)}**
- The inputs are 1, 2, -8, and 0. Each input is different and corresponds to the same output (3).
- **Conclusion:** This relation is a function.
2. **Relation: {(4, 9), (-3, 1), (6, 3), (4, 3), (7, 14)}**
- The inputs are 4, -3, 6, 4, and 7. The input 4 is associated with two different outputs (9 and 3).
- **Conclusion:** This relation is not a function.
3. **Relation: {(3, 2.5), (8, -1.4), (4.5, -10), (3, 2.5), (1.2, 1.8)}**
- The inputs are 3, 8, 4.5, 3, and 1.2. The input 3 is associated with the output 2.5 twice, but that does not violate the function rule since it’s still only one output.
- **Conclusion:** This relation is a function.
4. **Relation: {(0, 0), (-1, 1), (-2, 2), (-3, 3), (-4, 4)}**
- The inputs are 0, -1, -2, -3, and -4. Each input is different and corresponds to a unique output.
- **Conclusion:** This relation is a function.
### Summary:
1. Function
2. Not a function
3. Function
4. Function
1. **Relation: {(1, 3), (2, 3), (-8, 3), (0, 3)}**
- The inputs are 1, 2, -8, and 0. Each input is different and corresponds to the same output (3).
- **Conclusion:** This relation is a function.
2. **Relation: {(4, 9), (-3, 1), (6, 3), (4, 3), (7, 14)}**
- The inputs are 4, -3, 6, 4, and 7. The input 4 is associated with two different outputs (9 and 3).
- **Conclusion:** This relation is not a function.
3. **Relation: {(3, 2.5), (8, -1.4), (4.5, -10), (3, 2.5), (1.2, 1.8)}**
- The inputs are 3, 8, 4.5, 3, and 1.2. The input 3 is associated with the output 2.5 twice, but that does not violate the function rule since it’s still only one output.
- **Conclusion:** This relation is a function.
4. **Relation: {(0, 0), (-1, 1), (-2, 2), (-3, 3), (-4, 4)}**
- The inputs are 0, -1, -2, -3, and -4. Each input is different and corresponds to a unique output.
- **Conclusion:** This relation is a function.
### Summary:
1. Function
2. Not a function
3. Function
4. Function
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