How could one write an expression/'function' for these graphs?

Sep 2012
Here are some graphs that I am aware are not technically functions.


I am trying to write 'functions' for them

My attempt:

A. Maybe I could write something like \(\displaystyle x = n \forall n \in \mathbb{N}\) and \(\displaystyle 0 \leq y \leq 1\). I don't know if this is a valid way to define a 'function'? Clearly if this is right then for B. the range for y could just be extended.

C. This should be something like \(\displaystyle y^2 = x\) but repeating every 1, and I'm not sure how I can do this.

Thanks in advance for your help.


MHF Helper
Sep 2012
Hey kinhew93.

Functions don't satisfy that property since a function has to only be defined to have one value for all input combinations.

So if you take an input combination [call it a vector V] then if f(V) has two possibilities it is not a function.

All of your above graphs are not a function if you try to use y = f(x).