What is the domain of a relation? What is the range of a relation? When is a relation a function?
Domain: {1, 2, 3, 4, 5 } Range: {11, 13, 15, 17 } Is It a Function?: Yes, see solution. Interpretation: See solution.
Practice makes perfect
We are given a relation between the number of hours a person is able to rent a canoe and the cost of renting the canoe for that many hours. First, let's identify the domain and range using the given representation. Then we can interpret these values in context and decide if the relation is a function.
Domain and Range
In a relation, we have ordered pairs (x, y), where the x-values are the inputs and the y-values are the outputs. The domain is all possible inputs for a relation, while the range is all possible outputs. By looking at the representations, we can see the ordered pairs of this relation. We can list these values to have the domain and range.
Domain:& {1, 2, 3, 4, 5 }
Range:& {11, 13, 15, 17 }
Interpretation of Data Points
Since the domain represents the number of hours a person is able to rent a canoe, the range represents the cost of renting the canoe for that many hours. We can also identify each output for its corresponding input in this context.
Renting the canoe for 1 hour costs $11.
Renting the canoe for 2 hours also costs $11.
Renting the canoe for 3 hours costs $13.
Renting the canoe for 4 hours costs $15.
Renting the canoe for 5 hours costs $17.
Is it a function?
We can see that this relation is a function because each value in the domain is paired with exactly one value in the range. This can be seen most clearly in the mapping diagram. There is one arrow originating from each x-value, which is what we need.
