I am trying to create a program that requires the graphing of a "non-function", i.e, a function where "x" isn't strictly dependent on "y".
Let's answer the obvious question: Is it even possible?
Yes, it is possible, as demonstrated by online graphing calculators such as Desmos and GeoGebra, as well as several other open-source softwares. However, I haven't had success in figuring out how these graphing calculators graph non-functions. I have done some research, and have found nothing helpful.
Now, I'm looking for means to graph any non-functions, not just simple ones such as a circle or a sideways parabola, which simply require the graphs of +f(x) and -f(x). Maybe more complicated ones such as sin(x) + sin(y)= 1. The following graph is of the said non-function, as graphed by Desmos.
Any help on how to graph non-functions is appreciated. Thanks in advance.
Best Answer
A lot of the time examples like these "look" like functions locally. Therefore they can broken up into little pieces by using a valid set of initial conditions or a function which is valid and describes part of the overall relation you are trying to graph.
In your example we can convert the equation to look like:
$$ y = sin^{-1}(1-sin(x)) $$
Which gives a starting point looking like the bottom half of a single warped sphere. Then we see that since $sin(y)=sin(\pi-y)$ we can cap the warped sphere. Then we can argue that the equation is clearly unchanged if we were to replace $(x,y)$ with $(x+2\pi n ,y+2\pi m)$ (for integer values of m,n) and so we can repeat our pattern throughout the entire grid due to the periodicity of the $sin$ function.
Another good example is $y^2 = x$ where we have two sets of solutions corresponding to $y=\pm \sqrt{x} $.