Which Set Of Ordered Pairs Does Not Represent A Function?A. \[$\{(-1,-3),(3,7),(-4,7),(-2,-2)\}\$\]B. \[$\{(2,4),(7,9),(-6,8),(-5,4)\}\$\]C. \[$\{(9,-2),(9,5),(-9,1),(3,0)\}\$\]D. \[$\{(-4,-8),(-2,7),(-5,-6),(3,7)\}\$\]

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In mathematics, a function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is a way of assigning each input to exactly one output. In other words, for every input, there is only one corresponding output. In this article, we will explore which set of ordered pairs does not represent a function.

Understanding Functions

A function is a relation between a set of inputs and a set of outputs. It is a way of assigning each input to exactly one output. For example, consider a simple function f(x) = 2x. This function takes an input x and assigns it to an output 2x. For every input x, there is only one corresponding output 2x.

Ordered Pairs and Functions

Ordered pairs are used to represent relations between two sets. They consist of an ordered pair (x, y), where x is the input and y is the output. For a relation to be a function, each input must correspond to exactly one output. In other words, for every input x, there must be only one corresponding output y.

Analyzing the Options

Let's analyze the given options to determine which set of ordered pairs does not represent a function.

Option A

  • Option A: {{(-1,-3),(3,7),(-4,7),(-2,-2)}$}$
  • Analysis: In this option, each input corresponds to exactly one output. For example, the input -1 corresponds to the output -3, and the input 3 corresponds to the output 7. Therefore, this set of ordered pairs represents a function.

Option B

  • Option B: {{(2,4),(7,9),(-6,8),(-5,4)}$}$
  • Analysis: In this option, each input corresponds to exactly one output. For example, the input 2 corresponds to the output 4, and the input -5 corresponds to the output 4. Therefore, this set of ordered pairs represents a function.

Option C

  • Option C: {{(9,-2),(9,5),(-9,1),(3,0)}$}$
  • Analysis: In this option, the input 9 corresponds to two different outputs: -2 and 5. This means that for the input 9, there are two corresponding outputs, which is not allowed in a function. Therefore, this set of ordered pairs does not represent a function.

Option D

  • Option D: {{(-4,-8),(-2,7),(-5,-6),(3,7)}$}$
  • Analysis: In this option, each input corresponds to exactly one output. For example, the input -4 corresponds to the output -8, and the input 3 corresponds to the output 7. Therefore, this set of ordered pairs represents a function.

Conclusion

In conclusion, the set of ordered pairs that does not represent a function is Option C: {{(9,-2),(9,5),(-9,1),(3,0)}$}$. This is because the input 9 corresponds to two different outputs: -2 and 5, which is not allowed in a function.

Key Takeaways

  • A function is a relation between a set of inputs and a set of outputs.
  • For a relation to be a function, each input must correspond to exactly one output.
  • Ordered pairs are used to represent relations between two sets.
  • A set of ordered pairs represents a function if each input corresponds to exactly one output.

Final Thoughts

In our previous article, we discussed which set of ordered pairs does not represent a function. In this article, we will answer some frequently asked questions (FAQs) about functions to help you better understand this concept.

Q: What is a function?

A: A function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is a way of assigning each input to exactly one output.

Q: What are the characteristics of a function?

A: The characteristics of a function are:

  • Each input corresponds to exactly one output.
  • For every input, there is only one corresponding output.
  • The output is determined by the input.

Q: What is the difference between a function and a relation?

A: A relation is a set of ordered pairs that shows the relationship between two sets. A function is a special type of relation where each input corresponds to exactly one output.

Q: Can a function have multiple outputs for the same input?

A: No, a function cannot have multiple outputs for the same input. If a function has multiple outputs for the same input, it is not a function.

Q: Can a function have no output for a given input?

A: Yes, a function can have no output for a given input. This is known as a "hole" in the function.

Q: Can a function have multiple inputs that correspond to the same output?

A: Yes, a function can have multiple inputs that correspond to the same output. This is known as a "vertical line" in the function.

Q: How do you determine if a relation is a function?

A: To determine if a relation is a function, you need to check if each input corresponds to exactly one output. If each input corresponds to exactly one output, then the relation is a function.

Q: What is the domain and range of a function?

A: The domain of a function is the set of all possible inputs. The range of a function is the set of all possible outputs.

Q: Can the domain and range of a function be the same?

A: Yes, the domain and range of a function can be the same. This is known as a "one-to-one" function.

Q: Can the domain and range of a function be different?

A: Yes, the domain and range of a function can be different. This is known as a "many-to-one" function.

Q: What is the difference between a one-to-one function and a many-to-one function?

A: A one-to-one function is a function where the domain and range are the same. A many-to-one function is a function where the domain and range are different.

Q: Can a function be both one-to-one and many-to-one?

A: No, a function cannot be both one-to-one and many-to-one. A function is either one-to-one or many-to-one, but not both.

Q: What is the importance of functions in mathematics?

A: Functions are important in mathematics because they help us model real-world situations and solve problems. Functions are used in various fields, including science, engineering, and economics.

Q: Can functions be used in real-world applications?

A: Yes, functions can be used in real-world applications. Functions are used in various fields, including science, engineering, and economics.

Conclusion

In conclusion, functions are an important concept in mathematics. Understanding functions is crucial for solving problems in various fields, including science, engineering, and economics. We hope that this article has helped you better understand functions and their characteristics.

Key Takeaways

  • A function is a relation between a set of inputs and a set of outputs.
  • Each input corresponds to exactly one output in a function.
  • The domain and range of a function are the set of all possible inputs and outputs, respectively.
  • A function can be one-to-one or many-to-one, but not both.
  • Functions are used in various fields, including science, engineering, and economics.

Final Thoughts

In this article, we answered some frequently asked questions (FAQs) about functions to help you better understand this concept. We hope that this article has helped you better understand functions and their characteristics. If you have any more questions, feel free to ask!