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: {50, 100, 150, 200 } Is It a Function?: Yes, see solution. Interpretation: See solution.
Practice makes perfect
We have the relation between the time driven in hours and the number of miles traveled at the end of each hour. 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 representation, 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:& {50, 100, 150, 200 }
Interpretation of Data Points
Since the domain represents the time driven in hours, the range represents the number of miles traveled at the end of each hour. We can also identify each output for its corresponding input in this context.
After 1 hour, the number of miles driven was 50.
After 2 hours, the number of miles driven was 100.
After 3 hours, the number of miles driven was 150.
After 4 hours, the number of miles driven was also 150. Apparently the driver stopped, possibly to rest or to repair the vehicle.
After 5 hours, the number of miles driven was 200.
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.
