What is the domain of a relation? What is the range of a relation? When is a relation a function?
Domain: {4, 8, 12, 16, 20 } Range: {1, 2, 3, 4 } Is It a Function?: No, see solution. Interpretation: See solution.
Practice makes perfect
We are given a graph representing the average soccer goals scored for players of different ages. 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.
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:& {4, 8, 12, 16, 20 }
Range:& {1, 2, 3, 4 }
Interpretation of Data Points
Since the domain represents the age of the players, the range represents the average soccer goals scored for them. We can also identify each output for its corresponding input in this context.
For a 4-year-old player, 1 soccer goal was scored on average.
For a 8-year-old player, 1 and 2 soccer goals was scored on average.
For a 12-year-old player, 2 and 3 soccer goals was scored on average.
For a 16-year-old player, 4 soccer goals was scored on average.
For a 20-year-old player, 3 soccer goals was scored on average.
Is it a function?
We can see that this relation is not a function because 8 and 12 are paired with two values in the range.
