Which Set Of Ordered Pairs Represents A Function?A. { {(2,-2),(1,5),(-2,2),(1,-3),(8,-1)}$}$B. { {(3,-1),(7,1),(-6,-1),(9,1),(2,-1)}$}$C. { {(6,8),(5,2),(-2,-5),(1,-3),(-2,9)}$}$D.
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 describing a relationship between two sets of values, where each input value corresponds to exactly one output value. In this article, we will explore which set of ordered pairs represents a function.
Understanding Functions
A function is a relation between two sets of values, where each input value corresponds to exactly one output value. This means that for every input value, there is only one corresponding output value. In other words, a function is a way of describing a relationship between two sets of values, where each input value is associated with only one output value.
Ordered Pairs and Functions
Ordered pairs are a way of representing a relation between two sets of values. They consist of two values, one from each set, that are paired together. For example, the ordered pair (2, 5) represents a relation between the input value 2 and the output value 5.
Analyzing the Options
Let's analyze the four options given:
A. {{(2,-2),(1,5),(-2,2),(1,-3),(8,-1)}$}$
This set of ordered pairs has two input values, 1 and 2, that correspond to the same output value, 5 and -3 respectively. This means that this set of ordered pairs does not represent a function, as each input value is associated with more than one output value.
B. {{(3,-1),(7,1),(-6,-1),(9,1),(2,-1)}$}$
This set of ordered pairs has two input values, 7 and 9, that correspond to the same output value, 1. This means that this set of ordered pairs does not represent a function, as each input value is associated with more than one output value.
C. {{(6,8),(5,2),(-2,-5),(1,-3),(-2,9)}$}$
This set of ordered pairs has two input values, -2 and 1, that correspond to the same output value, -5 and -3 respectively. This means that this set of ordered pairs does not represent a function, as each input value is associated with more than one output value.
D. {{(4,6),(3,7),(2,8),(1,9),(0,10)}$}$
This set of ordered pairs has five input values, 0, 1, 2, 3, and 4, that correspond to the output values 10, 9, 8, 7, and 6 respectively. This means that this set of ordered pairs represents a function, as each input value is associated with only one output value.
Conclusion
In conclusion, the set of ordered pairs that represents a function is option D. {{(4,6),(3,7),(2,8),(1,9),(0,10)}$}$. This set of ordered pairs has five input values, 0, 1, 2, 3, and 4, that correspond to the output values 10, 9, 8, 7, and 6 respectively. This means that each input value is associated with only one output value, making it a function.
Key Takeaways
- A function is a relation between a set of inputs and a set of possible outputs, where each input value corresponds to exactly one output value.
- Ordered pairs are a way of representing a relation between two sets of values.
- A set of ordered pairs represents a function if each input value is associated with only one output value.
Frequently Asked Questions
- What is a function? A function is a relation between a set of inputs and a set of possible outputs, where each input value corresponds to exactly one output value.
- What is an ordered pair? An ordered pair is a way of representing a relation between two sets of values, consisting of two values, one from each set, that are paired together.
- How do I determine if a set of ordered pairs represents a function?
To determine if a set of ordered pairs represents a function, check if each input value is associated with only one output value. If each input value is associated with more than one output value, the set of ordered pairs does not represent a function.
Frequently Asked Questions: Functions and Ordered Pairs =====================================================
In our previous article, we explored which set of ordered pairs represents a function. In this article, we will answer some frequently asked questions about functions and ordered pairs.
Q: What is a function?
A: A function is a relation between a set of inputs and a set of possible outputs, where each input value corresponds to exactly one output value.
Q: What is an ordered pair?
A: An ordered pair is a way of representing a relation between two sets of values, consisting of two values, one from each set, that are paired together.
Q: How do I determine if a set of ordered pairs represents a function?
A: To determine if a set of ordered pairs represents a function, check if each input value is associated with only one output value. If each input value is associated with more than one output value, the set of ordered pairs does not represent a function.
Q: What is the difference between a function and a relation?
A: A function is a relation between a set of inputs and a set of possible outputs, where each input value corresponds to exactly one output value. A relation, on the other hand, is a set of ordered pairs that may have multiple output values for a single input value.
Q: Can a function have multiple output values for a single input value?
A: No, a function cannot have multiple output values for a single input value. By definition, a function is a relation between a set of inputs and a set of possible outputs, where each input value corresponds to exactly one output value.
Q: Can a relation have multiple input values for a single output value?
A: Yes, a relation can have multiple input values for a single output value. This is because a relation is a set of ordered pairs that may have multiple output values for a single input value.
Q: How do I graph a function?
A: To graph a function, you can use a coordinate plane and plot the ordered pairs that make up the function. You can also use a graphing calculator or software to graph the function.
Q: What is the domain of a function?
A: The domain of a function is the set of all possible input values for the function.
Q: What is the range of a function?
A: The range of a function is the set of all possible output values for the function.
Q: Can a function have an empty domain or range?
A: Yes, a function can have an empty domain or range. For example, the function f(x) = 1/x has an empty domain because it is not defined for x = 0.
Q: Can a function have a single output value for all input values?
A: Yes, a function can have a single output value for all input values. For example, the function f(x) = 0 has a single output value of 0 for all input values.
Conclusion
In conclusion, functions and ordered pairs are fundamental concepts in mathematics. Understanding the difference between a function and a relation, and how to determine if a set of ordered pairs represents a function, is crucial for success in mathematics. We hope this article has helped to clarify any questions you may have had about functions and ordered pairs.
Key Takeaways
- A function is a relation between a set of inputs and a set of possible outputs, where each input value corresponds to exactly one output value.
- An ordered pair is a way of representing a relation between two sets of values, consisting of two values, one from each set, that are paired together.
- To determine if a set of ordered pairs represents a function, check if each input value is associated with only one output value.
- A function can have multiple output values for a single input value, but a relation can have multiple input values for a single output value.
- The domain of a function is the set of all possible input values for the function, and the range of a function is the set of all possible output values for the function.