A question on plotting functions on a graph

[#neutrino]

when i was reading a supplementary notes doc from open course ware fro MIT on single variable calculus there was a description about a graphical representation of a single valued function as
" if each line parallel to the y- axis and which passes through a point in the domain intersects the graph at only one point then our function is single valued " my point is since it is a line drawn parallel to the y- axis for each input there will be several outputs ,therefore how come it is a function at all?

 

[theodoros.mihos]

It is not function. It is just a line.

 

[Samy_A]

when i was reading a supplementary notes doc from open course ware fro MIT on single variable calculus there was a description about a graphical representation of a single valued function as
" if each line parallel to the y- axis and which passes through a point in the domain intersects the graph at only one point then our function is single valued " my point is since it is a line drawn parallel to the y- axis for each input there will be several outputs ,therefore how come it is a function at all?

It's nothing more than a question of terminology.
Currently a function is defined as single valued. In certain applications one uses the concept multivalued functions (complex logarithm for example).

Apparently our current definition of function has changed with time.

From Wikipedia:

The practice of allowing function in mathematics to mean also multivalued function dropped out of usage at some point in the first half of the twentieth century. Some evolution can be seen in different editions of A Course of Pure Mathematics by G. H. Hardy, for example.
It probably persisted longest in the theory of special functions, for its occasional convenience.