What Are The Domain And Range Of This Relation?$\[ \begin{array}{l} (-2,0) \\ (2,-1) \\ (-9,8) \\ (2,-4) \end{array} \\]Options For Domain:A. \[$\{-9, -2, 0, 2\}\$\]B. \[$\{-9, -2, 2\}\$\]Options For Range:C. \[$\{-4, -1,

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In mathematics, a relation is a set of ordered pairs that describe the relationship between two variables. The domain and range of a relation are essential concepts that help us understand the properties and behavior of the relation. In this article, we will explore the domain and range of a given relation and discuss the options provided.

What is the Domain of a Relation?

The domain of a relation is the set of all possible input values or x-coordinates of the ordered pairs in the relation. It represents the values that the independent variable can take. In other words, the domain is the set of all possible x-values that make the relation true.

What is the Range of a Relation?

The range of a relation is the set of all possible output values or y-coordinates of the ordered pairs in the relation. It represents the values that the dependent variable can take. In other words, the range is the set of all possible y-values that make the relation true.

Given Relation

The given relation is a set of ordered pairs:

{ \begin{array}{l} (-2,0) \\ (2,-1) \\ (-9,8) \\ (2,-4) \end{array} \}

Domain of the Relation

To find the domain of the relation, we need to identify the unique x-values in the ordered pairs. In this case, the x-values are -2, 2, -9, and 2. However, we need to eliminate any duplicate values. Since -2 and 2 are repeated, we only consider them once.

The domain of the relation is the set of all unique x-values:

{−9,−2,2}{ \{-9, -2, 2\} }

Range of the Relation

To find the range of the relation, we need to identify the unique y-values in the ordered pairs. In this case, the y-values are 0, -1, 8, and -4. However, we need to eliminate any duplicate values. Since 0 and -1 are not repeated, we consider them as unique values. However, 8 is not present in the given options.

The range of the relation is the set of all unique y-values:

{−4,−1,0}{ \{-4, -1, 0\} }

Conclusion

In conclusion, the domain of the given relation is {−9,−2,2}\{-9, -2, 2\}, and the range is {−4,−1,0}\{-4, -1, 0\}. Therefore, the correct options for the domain and range are:

  • Domain: {−9,−2,2}\boxed{\{-9, -2, 2\}}
  • Range: {−4,−1,0}\boxed{\{-4, -1, 0\}}

Discussion

The given relation is a set of ordered pairs that describe the relationship between two variables. The domain and range of the relation are essential concepts that help us understand the properties and behavior of the relation. In this article, we explored the domain and range of the given relation and discussed the options provided.

The domain of the relation is the set of all unique x-values, which is {−9,−2,2}\{-9, -2, 2\}. The range of the relation is the set of all unique y-values, which is {−4,−1,0}\{-4, -1, 0\}. Therefore, the correct options for the domain and range are:

  • Domain: {−9,−2,2}\boxed{\{-9, -2, 2\}}
  • Range: {−4,−1,0}\boxed{\{-4, -1, 0\}}

References

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