Example 1
: Determine if the given relation is function or not. Give its
domain and range. {(1, 2), (1, -2), (2, 3), (3, 4)}
Is this a function or not?
We need to ask ourselves, does every first element (or input) correspond with
EXACTLY ONE
second element (or output)? In this case, the answer is
no. The input value of 1 goes with two output values, 2 and -2. It only takes
one input value to associate with more than one output value to be invalid as
a function.
So, this relation would not be an example of a function.
Domain
We need to find the set of all input values. In terms of ordered pairs, that correlates with the first
component of each one. So, what do you get for the domain?
If you got {1, 2, 3}, you are correct!
Note that if any value repeats, we only need to list it one time.
Range
We need to find the set of all output values. In terms of ordered pairs, that correlates with the
second component of each one. So, what do you get for the range?
If you got {2, -2, 3, 4}, you are absolutely right!
Example 2
: Determine if the given relation is function or not. Give its
domain and range. {(5, 10), (10, 10), (15, 10)}