What is the domain of a relation? What is the range of a relation? When is a relation a function?
See solution.
Practice makes perfect
We have three different representations for the relation between the time spent exercising and the number of calories burned during that time. First, let's identify the domain and range using the given representations. Then we can interpret these values in context and decide if the relation is a function.
Time (min)
Calories burned
20
50
30
85
35
85
60
100
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: {20, 30, 35, 60 }
Range: {50, 85, 100}
Interpretation of Data Points
Since the domain represents time spent exercising, the range represents the calories burned during that time. We can also identify each output for its corresponding input in this context.
For an input of 20 minutes exercising, we have an output of 50.
For an input of 30 minutes exercising , we have an output of 85.
For an input of 35 minutes exercising, we have an output of 85.
For an input of 60 minutes exercising, we have an output of 100.
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.
