Graph of two variables function one of which depends on the other

Question

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!

Answer 1

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')