Identify the following given the relation below.
{(1, 6), (2, 7), (3, 8), (4, 9), (5, 10)}
(3 points)
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Range
Function
Domain
The given relation {(1, 6), (2, 7), (3, 8), (4, 9), (5, 10)} can be identified as a function because each input (x-value) corresponds to exactly one output (y-value).
The correct answer is:
Domain: {1, 2, 3, 4, 5}
The domain of a relation is the set of all input values, or the x-values in this case. In this relation, the first number in each ordered pair represents the input values, so the domain will be {1, 2, 3, 4, 5}.
To identify the given relation, we need to understand the terms "range," "function," and "domain." Let me explain each one to you:
1. Range: The range of a function represents all the possible outputs or y-values of the relation. In other words, it is the set of values that the dependent variable can take on. To find the range, we need to look at the second element of each ordered pair in the relation.
2. Function: A function is a relation between two sets, where each input (x-value) is associated with exactly one output (y-value). In simpler terms, it means that for each value of x, there is only one corresponding value of y. To determine if the given relation is a function, we need to check if every x-value has a unique y-value associated with it.
3. Domain: The domain of a function represents all the possible inputs or x-values of the relation. In other words, it is the set of values that the independent variable can take on. To find the domain, we need to look at the first element of each ordered pair in the relation.
Now that we understand these terms, let's apply them to the given relation:
{(1, 6), (2, 7), (3, 8), (4, 9), (5, 10)}
- Range: To determine the range, we look at the second element of each pair: {6, 7, 8, 9, 10}. Therefore, the range is {6, 7, 8, 9, 10}.
- Function: In this relation, each x-value has a unique y-value associated with it. So, it is a function.
- Domain: To find the domain, we look at the first element of each pair: {1, 2, 3, 4, 5}. Therefore, the domain is {1, 2, 3, 4, 5}.
Identifying the given relation with respect to range, function, and domain, we have:
Range: {6, 7, 8, 9, 10}
Function: Yes, it is a function.
Domain: {1, 2, 3, 4, 5}