Select The Correct Answer.What Is The Domain Of The Set Of Ordered Pairs Below?$\[ \begin{tabular}{c} $(-1, 1)$ \\ $(0, -1)$ \\ $(5, -11)$ \\ $(10, -21)$ \end{tabular} \\]A. $\{-1, 0, 5, 10\}$B. $\{1, 0, 5, 10\}$C.
When dealing with a set of ordered pairs, it's essential to understand the concept of the domain. The domain of a set of ordered pairs refers to the set of all possible first elements or x-coordinates of the pairs. In other words, it's the collection of all unique x-values that appear in the ordered pairs.
What is the Domain of a Set of Ordered Pairs?
To determine the domain of a set of ordered pairs, we need to identify the unique x-values that appear in the pairs. Let's take a closer look at the given set of ordered pairs:
{ \begin{tabular}{c} $(-1, 1)$ \\ $(0, -1)$ \\ $(5, -11)$ \\ $(10, -21)$ \end{tabular} \}
Identifying the Unique x-Values
As we can see, the x-values in the given set of ordered pairs are -1, 0, 5, and 10. These are the unique x-values that appear in the pairs.
Determining the Domain
Since the domain is the set of all unique x-values, we can conclude that the domain of the given set of ordered pairs is the set of all unique x-values, which are -1, 0, 5, and 10.
Conclusion
In conclusion, the domain of a set of ordered pairs is the set of all unique x-values that appear in the pairs. By identifying the unique x-values, we can determine the domain of the set of ordered pairs.
Answer
Based on the analysis above, the correct answer is:
A. ${-1, 0, 5, 10}$
This is the set of all unique x-values that appear in the given set of ordered pairs.
Why is this the Correct Answer?
This is the correct answer because the domain of a set of ordered pairs is the set of all unique x-values that appear in the pairs. In this case, the unique x-values are -1, 0, 5, and 10, which are the elements of the set ${-1, 0, 5, 10}$.
What is the Importance of Domain in Mathematics?
The domain of a set of ordered pairs is an essential concept in mathematics, particularly in algebra and geometry. Understanding the domain helps us to:
- Identify the range of possible values for a function
- Determine the x-intercepts of a graph
- Solve equations and inequalities involving functions
- Understand the behavior of functions and their graphs
Real-World Applications of Domain
The concept of domain has numerous real-world applications in fields such as:
- Computer programming: Understanding the domain of a function helps programmers to write efficient and effective code.
- Data analysis: Identifying the domain of a dataset helps analysts to understand the range of possible values and make informed decisions.
- Engineering: Understanding the domain of a function helps engineers to design and optimize systems.
Conclusion
Frequently Asked Questions
In this article, we'll address some of the most common questions related to the domain of a set of ordered pairs.
Q: What is the domain of a set of ordered pairs?
A: The domain of a set of ordered pairs is the set of all unique x-values that appear in the pairs.
Q: How do I determine the domain of a set of ordered pairs?
A: To determine the domain of a set of ordered pairs, you need to identify the unique x-values that appear in the pairs. Simply look at the x-coordinates of each pair and list the unique values.
Q: What if there are multiple x-values with the same value?
A: If there are multiple x-values with the same value, you should only include that value once in the domain. For example, if you have the pairs (2, 3) and (2, 4), the domain would be {2}.
Q: Can the domain be a set of real numbers?
A: Yes, the domain of a set of ordered pairs can be a set of real numbers. For example, if you have the pairs (1.5, 2) and (3.7, 4), the domain would be {1.5, 3.7}.
Q: Can the domain be a set of integers?
A: Yes, the domain of a set of ordered pairs can be a set of integers. For example, if you have the pairs (2, 3) and (5, 6), the domain would be {2, 5}.
Q: How does the domain relate to the range of a function?
A: The domain of a function is the set of all possible input values, while the range is the set of all possible output values. The domain and range are related in that the domain of a function determines the possible output values.
Q: Can the domain be empty?
A: Yes, the domain of a set of ordered pairs can be empty. For example, if you have no pairs, the domain would be the empty set {}.
Q: Can the domain be a set of complex numbers?
A: Yes, the domain of a set of ordered pairs can be a set of complex numbers. For example, if you have the pairs (2 + 3i, 4) and (5 - 2i, 6), the domain would be {2 + 3i, 5 - 2i}.
Q: How does the domain affect the graph of a function?
A: The domain of a function affects the graph of the function by determining the x-values that are included in the graph. If the domain is restricted, the graph will only include those x-values.
Q: Can the domain be a set of rational numbers?
A: Yes, the domain of a set of ordered pairs can be a set of rational numbers. For example, if you have the pairs (1/2, 3) and (3/4, 6), the domain would be {1/2, 3/4}.
Conclusion
In conclusion, the domain of a set of ordered pairs is the set of all unique x-values that appear in the pairs. Understanding the concept of domain is essential in mathematics and has numerous real-world applications. By identifying the unique x-values, we can determine the domain of the set of ordered pairs and make informed decisions in various fields.