I'm working through multivariable functions and derivatives of multivariable functions. Since I am not very familiar yet with multivariable functions I wondered about the following:
In a function like $f(x,y)=x^2+y$, are x and y independent of each other and are we allowed to pick values for each deliberately?
Say for 1 for x and 99 for y?
As far as I have understood that topic it seems to me that indeed I can deliberately pick any value and will get an output in a third dimension. Rather than a curve I will receive a surface representing every possible combination of x and y. As long as the function is not limited like the equation for a circle, $x^2+y^2=r^2$. But I am not sure if I concluded this correctly.
I guess it's a pretty easy or maybe even silly question but I haven't fully figured that out yet.