Vertical line test 
A vertical line crossing the x-axis at a point $a$ will meet the set in exactly one point $(a, b)$ if $f(a)$ is defined, and $f(a) = b$.

If the vertical line meets the set of points in two points then $f(a)$ is undefined? 

The highlighted proposition is one way of describing the vertical line test, which determines whether $f$ is a function. 
If there is one and only point of intersection between $x = a$ and $f(x)$, then $f$ is a function. 
If there are two or more points of intersection between $x = a$ and $f(x)$, then $f$ maps a given $x = a$ to two (or more) distinct values, $f(a) = b, f(a) = c, \; b \neq c$, and hence, fails to be a function, by definition of a function. $f$ may, however, a relation.
