I am a mathematical beginner. As we all know, the graph of a one-dimensional function is a curve, and the graph of a two-dimensional function is a surface. What is the graph of a three-dimensional function? For example, $f(x,y,z)=x^2+y^3+5xyz$. Someone said that we cannot draw the graph of a three-dimensional function. Could someone explain why? Thank you in advance for your kind help.
I mean the answer is we can visualise them, but it's just not possible to draw them! Obviously , the limitation here is that a three dimensional function actually delves into the fourth dimension, whereas we obviously live in a 3D space and so it's not possible for us to draw such a function.
However, a nice representation of a 3 dimensional function could be to set one of the variables to time, and see how the shape of the graph changes throughout time. (which closely links to the ideas of level sets)
That is not to say that we can't analyse such functions, it is just significantly harder to visualise them.