Domain: {11, 12, 13, 15, 16 } Range: {7, 8, 10, 10.5, 11 } Is It a Function? No, see solution.
Practice makes perfect
For the given table, we need to find the domain and range, interpret them in context, and then decide if it is a function.
Age
Shoe size
x
y
11
7
12
8
13
10
15
10
15
10.5
16
11
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. Looking at the table, we can see the ordered pairs of this relation. Listing these values gives us the domain and range.
Domain:& {11, 12, 13, 15, 16 }
Range:& {7, 8, 10, 10.5, 11 }
Interpretation of Data Points
Since the domain represents the age of the people, the range represents their corresponding shoe size. We can identify each output for its corresponding input in this context.
For an input of 11 years old, we have an output of 7 in shoe size.
For an input of 12 years old, we have an output of 8 in shoe size.
For an input of 13 years old, we have an output of 10 in shoe size.
For an input of 15 years old, we have outputs of 10 and 10.5 in shoe size.
For an input of 16 years old, we have an output of 11 in shoe size.
Is it a Function?
Recall that a relation can be a function only if no more than one output value is being assigned to any input value. We can see that this relation is not a function because the input value 15 is paired with two output values in the range, 10 and 10.5.
