Let's recall each method and point out in which circumstances they would be easier to use.
Mapping Diagram
To make a mapping diagram, we need to write all the elements of the domain and all the elements of the range. Then, we match the corresponding values using arrows. If any element of the domain is not mapped to exactly one element of the range, then the relation is not a function.
This method is useful when the relation
is given as a set of ordered pairs.
Let's see some examples.
Examples
Let's determine if any of the following relations, given a sets of ordered pairs, represents a function.
Relation I: { (1,2), (2,4), (3,6) }
Relation II: { (1,2), (2,4), (2,6) }
We will now make a mapping diagram for each relation.
In the first relation, every input value has exactly one output value. Therefore, Relation I is a function. Conversely, in the second relation, there is an input value with more than one output. This means that Relation II is not a function.
Vertical Line Test
This method consists of drawing a vertical line across the graph of the relation. For every input value, if the vertical line intersects the graph at only one point, then the relation is a function. If for at least one input value the vertical line intersects the graph of the relation more than once, then the relation is not a function.
This method is useful when the
relation is given as a graph.
Let's see some examples.
Examples
We will analyze the graph of two relations using the Vertical Line Test.
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