Answer
If a vertical line parallel to the y-axis is drawn at any point on the graph and cuts the graph not more than once, then the graph represents a function.
Work Step by Step
Let R be a relation from set ${{S}_{1}}$ to set ${{S}_{2}}$ with ordered pair $\left( x,y \right)$.
A relation can be of four types:
(a) One–one relation: For one x, there is only one y.
(b) Many–one relation: For many x, there is one y.
(c) One–many relation: For one x, there are many y.
(d) Many–many relation: For many x, there are many y.
For the ordered pair $\left( x,y \right)$ in the relation R, if by putting one value of x only one value of y is obtained, then the relation is said to be a function. More than one value of x can give the same value of y without violating the definition of a function.
Hence, a one–one relation and a many–one relation are functions.
An example of a relation that is also a function is
$y=x$
An example of a relation that is not a function is
$\begin{align}
& {{y}^{2}}=x \\
& y=\pm \sqrt{x}
\end{align}$
The graph represented by ${{y}^{2}}=x$ is as follows:
