Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To determine if each set of ordered pairs represents a function, we need to check if every input (or x-value) is associated with exactly one output (or y-value). This means no x-value should repeat with a different y-value.
Let's analyze each set of ordered pairs one by one:
1. [tex]\((2, 3), (6, -5), (-1, 3)\)[/tex]
- Check the x-values: 2, 6, -1
- None of these x-values repeat.
- Since each x-value is unique, this set of ordered pairs represents a function.
2. [tex]\((1, 9), (-3, -2), (1, -4)\)[/tex]
- Check the x-values: 1, -3, 1
- The x-value 1 repeats, with different y-values (9 and -4).
- Since there is a repeated x-value with different y-values, this set does not represent a function.
3. [tex]\((7, -4), (0, 9), (2, -2)\)[/tex]
- Check the x-values: 7, 0, 2
- None of these x-values repeat.
- Since each x-value is unique, this set of ordered pairs represents a function.
4. [tex]\((0, 3), (0, 7), (4, 0)\)[/tex]
- Check the x-values: 0, 0, 4
- The x-value 0 repeats, with different y-values (3 and 7).
- Since there is a repeated x-value with different y-values, this set does not represent a function.
5. [tex]\((-6, 5), (-5, 6), (8, 2)\)[/tex]
- Check the x-values: -6, -5, 8
- None of these x-values repeat.
- Since each x-value is unique, this set of ordered pairs represents a function.
Summarizing the results:
1. [tex]\((2, 3), (6, -5), (-1, 3)\)[/tex] - Function
2. [tex]\((1, 9), (-3, -2), (1, -4)\)[/tex] - Not a Function
3. [tex]\((7, -4), (0, 9), (2, -2)\)[/tex] - Function
4. [tex]\((0, 3), (0, 7), (4, 0)\)[/tex] - Not a Function
5. [tex]\((-6, 5), (-5, 6), (8, 2)\)[/tex] - Function
Let's analyze each set of ordered pairs one by one:
1. [tex]\((2, 3), (6, -5), (-1, 3)\)[/tex]
- Check the x-values: 2, 6, -1
- None of these x-values repeat.
- Since each x-value is unique, this set of ordered pairs represents a function.
2. [tex]\((1, 9), (-3, -2), (1, -4)\)[/tex]
- Check the x-values: 1, -3, 1
- The x-value 1 repeats, with different y-values (9 and -4).
- Since there is a repeated x-value with different y-values, this set does not represent a function.
3. [tex]\((7, -4), (0, 9), (2, -2)\)[/tex]
- Check the x-values: 7, 0, 2
- None of these x-values repeat.
- Since each x-value is unique, this set of ordered pairs represents a function.
4. [tex]\((0, 3), (0, 7), (4, 0)\)[/tex]
- Check the x-values: 0, 0, 4
- The x-value 0 repeats, with different y-values (3 and 7).
- Since there is a repeated x-value with different y-values, this set does not represent a function.
5. [tex]\((-6, 5), (-5, 6), (8, 2)\)[/tex]
- Check the x-values: -6, -5, 8
- None of these x-values repeat.
- Since each x-value is unique, this set of ordered pairs represents a function.
Summarizing the results:
1. [tex]\((2, 3), (6, -5), (-1, 3)\)[/tex] - Function
2. [tex]\((1, 9), (-3, -2), (1, -4)\)[/tex] - Not a Function
3. [tex]\((7, -4), (0, 9), (2, -2)\)[/tex] - Function
4. [tex]\((0, 3), (0, 7), (4, 0)\)[/tex] - Not a Function
5. [tex]\((-6, 5), (-5, 6), (8, 2)\)[/tex] - Function
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.