Determining if the Ordered Pairs Represent a Function

Oct 13, 2025 by magicalceylontours.com 23 views

Introduction

In mathematics, a function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. A function is a way of describing a relationship between two sets of values, where each input value corresponds to exactly one output value. In this article, we will determine if the given ordered pairs represent a function.

What is a Function?

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 describing a relationship between two sets of values, where each input value corresponds to exactly one output value. In other words, for every input value, there is only one corresponding output value.

The Ordered Pairs

The given ordered pairs are: $\{(1,3),(4,12),(5,15),(6,18)\}$ . To determine if these ordered pairs represent a function, we need to check if each input value corresponds to exactly one output value.

Checking for a Function

To check if the ordered pairs represent a function, we need to check if each input value corresponds to exactly one output value. We can do this by checking if each input value is unique and if each output value is unique.

Input Values: The input values are 1, 4, 5, and 6. These values are unique, so we can proceed to check the output values.
Output Values: The output values are 3, 12, 15, and 18. These values are also unique, so we can proceed to check if each input value corresponds to exactly one output value.

Determining if the Ordered Pairs Represent a Function

To determine if the ordered pairs represent a function, we need to check if each input value corresponds to exactly one output value. We can do this by checking if each input value is paired with only one output value.

Input Value 1: The input value 1 is paired with the output value 3.
Input Value 4: The input value 4 is paired with the output value 12.
Input Value 5: The input value 5 is paired with the output value 15.
Input Value 6: The input value 6 is paired with the output value 18.

Since each input value is paired with only one output value, we can conclude that the ordered pairs represent a function.

Conclusion

In conclusion, the ordered pairs $\{(1,3),(4,12),(5,15),(6,18)\}$ represent a function because each input value corresponds to exactly one output value. This means that for every input value, there is only one corresponding output value.

Answer

The answer is: A. Yes

Final Thoughts

Introduction

In our previous article, we determined if the given ordered pairs represent a function. We checked if each input value corresponds to exactly one output value and found that the ordered pairs represent a function. In this article, we will provide a Q&A section to help you better understand the concept of functions and how to determine if ordered pairs represent a function.

Q&A

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 describing a relationship between two sets of values, where each input value corresponds to exactly one output value.

Q: What are the characteristics of a function?

A: The characteristics of a function are:

Each input value corresponds to exactly one output value.
Each output value corresponds to exactly one input value.
For every input value, there is only one corresponding output value.

Q: How do I determine if ordered pairs represent a function?

A: To determine if ordered pairs represent a function, you need to check if each input value corresponds to exactly one output value. You can do this by checking if each input value is unique and if each output value is unique.

Q: What if an input value is paired with more than one output value?

A: If an input value is paired with more than one output value, then the ordered pairs do not represent a function.

Q: What if an output value is paired with more than one input value?

A: If an output value is paired with more than one input value, then the ordered pairs do not represent a function.

Q: Can a function have multiple output values for the same input value?

A: No, a function cannot have multiple output values for the same input value. Each input value must correspond to exactly one output value.

Q: Can a function have multiple input values for the same output value?

A: No, a function cannot have multiple input values for the same output value. Each output value must correspond to exactly one input value.

Q: How do I represent a function using ordered pairs?

A: To represent a function using ordered pairs, you need to ensure that each input value corresponds to exactly one output value. You can do this by checking if each input value is unique and if each output value is unique.

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

A: A function is a relation where each input value corresponds to exactly one output value. A relation is a set of ordered pairs where each input value may correspond to more than one output value.

Q: Can a relation be a function?

A: Yes, a relation can be a function if each input value corresponds to exactly one output value.

Q: Can a function be a relation?

A: Yes, a function is a type of relation where each input value corresponds to exactly one output value.

Conclusion

In conclusion, determining if ordered pairs represent a function is an important concept in mathematics. By understanding the characteristics of a function and how to represent a function using ordered pairs, you can better understand the concept of functions and how to apply it in real-world scenarios.

Final Thoughts

In this article, we provided a Q&A section to help you better understand the concept of functions and how to determine if ordered pairs represent a function. We hope that this article has been helpful in clarifying any doubts you may have had about functions and ordered pairs.