Draw at different places of the coordinate plane. If one line the graph more than once, the relation is not a function. On the contrary, if no vertical line cuts the graph more than once, the relation is a function.
Notice that ℓ3 cuts the first graph at two different . Also, m2 passes through two different points. Then, neither Relation I nor Relation III is a function. In contrast, any vertical line cuts the graph of Relation II at most once. Thus, Relation II is a function.
- Relation I is not a function. ×
- Relation II is a function. ✓
- Relation III is not a function. ×
Keep in mind that, before stating that a relation is a function, the vertical lines drawn have to cover the entire to ensure that no vertical line cuts the graph more than once.