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The relation \( R \) is defined by the ordered pairs listed below. \( R=\{(2,-5),(-3,-20),(1,13),(1,-15),(-3,10)\} \) The domain of \( R \) is The range of \( R \) is Is \( R \) a function? O Yes, the relation is a function No, the relation is not a function Question Help: D Post to forum

Ask by Vaughan Huff. in the United States
Mar 25,2025

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Answer

The domain of \( R \) is \( \{2, -3, 1\} \), the range is \( \{-5, -20, 13, -15, 10\} \), and \( R \) is not a function.

Solution

To determine if the relation \( R \) is a function, we need to check if each element in the domain maps to a unique element in the range. Given relation \( R = \{(2,-5),(-3,-20),(1,13),(1,-15),(-3,10)\} \) Domain of \( R \): The set of all first elements in the ordered pairs, which are \( \{2, -3, 1\} \). Range of \( R \): The set of all second elements in the ordered pairs, which are \( \{-5, -20, 13, -15, 10\} \). To check if \( R \) is a function, we need to verify if each element in the domain maps to a unique element in the range. Since there are repeated elements in the range for the same element in the domain (e.g., \( (1,13) \) and \( (1,-15) \)), the relation \( R \) is not a function. Therefore, the answer is: No, the relation is not a function.

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The domain of the relation \( R \) consists of all the first elements from the ordered pairs, which are \( \{2, -3, 1\} \). This means the domain is unique values of inputs, leading to the set \( \{1, 2, -3\} \). Meanwhile, the range of \( R \) comprises the second elements of each pair: \( \{-5, -20, 13, -15, 10\} \). Thus, the range is \( \{-20, -15, -5, 10, 13\} \). Now, is \( R \) a function? Let's examine the definition of a function: each input should map to exactly one output. In this case, the input \( 1 \) is associated with two different outputs, \( 13 \) and \( -15 \). Therefore, the answer is: No, the relation is not a function.

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