What Is The Range Of The Relation In The Table Below?${ \begin{tabular}{|c|c|} \hline X X X & Y Y Y \ \hline -2 & 0 \ \hline -1 & 2 \ \hline 0 & 4 \ \hline 1 & 2 \ \hline 2 & 0 \ \hline \end{tabular} }$A. Range: ${0, 2, 4}$B.
Introduction
In mathematics, a relation is a set of ordered pairs that describe the relationship between two variables. When we have a table representing a relation, we can analyze the data to determine the range of the relation. The range of a relation is the set of all possible values of the second variable, which in this case is represented by the variable y. In this article, we will explore the concept of the range of a relation and how to determine it from a given table.
What is the Range of a Relation?
The range of a relation is the set of all possible values of the second variable, which in this case is represented by the variable y. In other words, it is the set of all values that y can take on. To determine the range of a relation, we need to look at the values of y in the table and identify the unique values that y can take on.
Analyzing the Table
Let's take a closer look at the table provided:
| x | y |
|---|---|
| -2 | 0 |
| -1 | 2 |
| 0 | 4 |
| 1 | 2 |
| 2 | 0 |
Identifying the Range
To determine the range of the relation, we need to look at the values of y in the table. We can see that y can take on the following values: 0, 2, and 4. These are the unique values that y can take on, and therefore, they are the values that make up the range of the relation.
Conclusion
In conclusion, the range of a relation is the set of all possible values of the second variable, which in this case is represented by the variable y. By analyzing the table provided, we can determine that the range of the relation is {0, 2, 4}. This means that y can take on the values 0, 2, and 4, and these are the values that make up the range of the relation.
Range of the Relation
The range of the relation is the set of all possible values of the second variable, which in this case is represented by the variable y. In other words, it is the set of all values that y can take on. To determine the range of a relation, we need to look at the values of y in the table and identify the unique values that y can take on.
Determining the Range
To determine the range of the relation, we need to follow these steps:
- Look at the values of y in the table.
- Identify the unique values that y can take on.
- The set of unique values that y can take on is the range of the relation.
Example
Let's take a closer look at the table provided:
| x | y |
|---|---|
| -2 | 0 |
| -1 | 2 |
| 0 | 4 |
| 1 | 2 |
| 2 | 0 |
We can see that y can take on the following values: 0, 2, and 4. These are the unique values that y can take on, and therefore, they are the values that make up the range of the relation.
Range of the Relation: {0, 2, 4}
The range of the relation is {0, 2, 4}. This means that y can take on the values 0, 2, and 4, and these are the values that make up the range of the relation.
Conclusion
In conclusion, the range of a relation is the set of all possible values of the second variable, which in this case is represented by the variable y. By analyzing the table provided, we can determine that the range of the relation is {0, 2, 4}. This means that y can take on the values 0, 2, and 4, and these are the values that make up the range of the relation.
Range of the Relation: A. Range: {0, 2, 4}
The range of the relation is {0, 2, 4}. This means that y can take on the values 0, 2, and 4, and these are the values that make up the range of the relation.
Range of the Relation: B. Range: {0, 2, 4}
The range of the relation is {0, 2, 4}. This means that y can take on the values 0, 2, and 4, and these are the values that make up the range of the relation.
Range of the Relation: Conclusion
In conclusion, the range of a relation is the set of all possible values of the second variable, which in this case is represented by the variable y. By analyzing the table provided, we can determine that the range of the relation is {0, 2, 4}. This means that y can take on the values 0, 2, and 4, and these are the values that make up the range of the relation.
Range of the Relation: Final Answer
Frequently Asked Questions
In this article, we will answer some of the most frequently asked questions about the range of a relation.
Q: What is the range of a relation?
A: The range of a relation is the set of all possible values of the second variable, which in this case is represented by the variable y.
Q: How do I determine the range of a relation?
A: To determine the range of a relation, you need to look at the values of y in the table and identify the unique values that y can take on.
Q: What if there are multiple values of y that are the same?
A: If there are multiple values of y that are the same, you only need to count each value once. For example, if y can take on the values 0, 2, and 4, and 2 appears twice in the table, you would still only count 2 once.
Q: Can the range of a relation be empty?
A: Yes, the range of a relation can be empty. This means that there are no values of y that appear in the table.
Q: Can the range of a relation have only one value?
A: Yes, the range of a relation can have only one value. This means that there is only one value of y that appears in the table.
Q: Can the range of a relation have multiple values?
A: Yes, the range of a relation can have multiple values. This means that there are multiple values of y that appear in the table.
Q: How do I know if the range of a relation is finite or infinite?
A: To determine if the range of a relation is finite or infinite, you need to look at the values of y in the table. If there are a finite number of values of y, then the range of the relation is finite. If there are an infinite number of values of y, then the range of the relation is infinite.
Q: Can the range of a relation be a subset of the domain?
A: Yes, the range of a relation can be a subset of the domain. This means that the values of y in the table are a subset of the values of x in the table.
Q: Can the range of a relation be equal to the domain?
A: Yes, the range of a relation can be equal to the domain. This means that the values of y in the table are equal to the values of x in the table.
Q: Can the range of a relation be a proper subset of the domain?
A: Yes, the range of a relation can be a proper subset of the domain. This means that the values of y in the table are a proper subset of the values of x in the table.
Q: Can the range of a relation be equal to the universal set?
A: Yes, the range of a relation can be equal to the universal set. This means that the values of y in the table are equal to the universal set.
Q: Can the range of a relation be a subset of the universal set?
A: Yes, the range of a relation can be a subset of the universal set. This means that the values of y in the table are a subset of the universal set.
Conclusion
In conclusion, the range of a relation is an important concept in mathematics that can be used to describe the relationship between two variables. By understanding the range of a relation, you can better analyze and describe the behavior of the variables in a relation.
Final Answer
The final answer is .