How will be the Graph of the function $f(x,y)$ where $y=ϕ(x)$.
From my intuition it seems it will not be a surface rather than a 3D curve! But I am not sure!
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Why do you think the two variables must be independent to generate a plot. Just define $x$, then calculate $y$, and finally $f(x,y) = z$:
%% Matlab code:
x = linspace(0,6*pi, 200);
y = sin(x);
[X, Y] = meshgrid(x,y);
Z = Y.^2 + cos(X);
figure(1);
plot3(X(:),Y(:),Z(:))
grid on;
xlabel('X')
ylabel('Y')
zlabel('Z')
Semoi
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Yes I have said about that! But That should be a 3D curve: because of the constraint $y=\phi(x)$. But in your graph it seems like it is a surface – PRITAM the cat of Newton Apr 05 '21 at 18:33