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QuestionFind the domain and range of the set {(1,2),(2,5),(3,1),(1,6),(4,8)}\{(1,2),(2,5),(3,1),(1,6),(4,8)\}. Is it a function?

Studdy Solution

STEP 1

Assumptions1. The given set is a set of ordered pairs. . The first element in each pair belongs to the domain and the second element belongs to the range.
3. A relation is a function if each element in the domain corresponds to exactly one element in the range.

STEP 2

First, we need to identify the domain of the given set. The domain is the set of all first elements in the ordered pairs.
Domain={x(x,y)∈{(1,2),(2,5),(,1),(1,6),(4,8)}}Domain = \{x (x, y) \in \{(1,2),(2,5),(,1),(1,6),(4,8)\}\}

STEP 3

List out the first elements from each ordered pair to form the domain.
Domain={1,2,3,1,}Domain = \{1,2,3,1,\}

STEP 4

Remove any duplicate elements from the domain. Each element in a set is unique.
Domain={1,2,3,4}Domain = \{1,2,3,4\}

STEP 5

Next, we need to identify the range of the given set. The range is the set of all second elements in the ordered pairs.
Range={y(x,y)∈{(1,2),(2,5),(3,1),(1,),(4,8)}}Range = \{y (x, y) \in \{(1,2),(2,5),(3,1),(1,),(4,8)\}\}

STEP 6

List out the second elements from each ordered pair to form the range.
Range={2,5,1,6,8}Range = \{2,5,1,6,8\}

STEP 7

Remove any duplicate elements from the range. Each element in a set is unique.
Range={2,5,1,6,}Range = \{2,5,1,6,\}

STEP 8

Now, we need to determine if the given set is a function. A relation is a function if each element in the domain corresponds to exactly one element in the range.We can see that the element '1' in the domain corresponds to '2' and '6' in the range. Therefore, the given set is not a function.
Domain {1,2,3,4}\{1,2,3,4\}Range {2,5,1,6,8}\{2,5,1,6,8\}The given set is not a function.

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