To determine if the set of ordered pairs \((0,0),(0,2),(0,3),(0,4)\) is a relation or a function, we need to recall the definitions of these terms.
-
A relation is simply a set of ordered pairs. Any set of ordered pairs qualifies as a relation.
-
A function is a specific type of relation where each input (the first element of the ordered pair) is associated with exactly one output (the second element of the ordered pair). In other words, no two ordered pairs can have the same first element with different second elements.
In this case, all ordered pairs have the same first element, which is \(0\), but they have different second elements: \(0\), \(2\), \(3\), and \(4\).
Since the input \(0\) is related to multiple outputs (specifically \(0, 2, 3,\) and \(4\)), this set does not meet the criteria to be a function.
Therefore, the set \((0,0),(0,2),(0,3),(0,4)\) is a relation but not a function.
1 answer