How can I plot $f(x, y) = x^2 + y^2$

$\begingroup$

I want to plot $f(x, y) = x^2 + y^2$? I can plot functions of a single variable but I don't know how to plot multivariable function.

$\endgroup$ 2

4 Answers

$\begingroup$

Your plot has three dimensions. You can plot it in perspective, in contour lines, or in various other representations. Alpha gives the following:

$\endgroup$ $\begingroup$

The graph of this function will be a surface in space. Above the point $(x,y)$ in the plane it has height $f(x,y)$.

$\endgroup$ $\begingroup$

In order to sketch this surface we need to consider$$z=x^2+y^2=(\text{distance of }(x,y)\text{ from }(0,0))^2$$So this is intuitively equivalent to the surface created by rotating the graph of $z=x^2$ about the $z$ axis.

$\endgroup$ $\begingroup$

Since the function $f(x,y)=x^2+y^2$ is from $\mathbb{R^2}$ to $\mathbb{R}$ we clearly need to visualise it in $\mathbb{R^{2+1}}$,and since the domain is $\mathbb{R^{2}}$ the graph will be a surface!! If you want to visualise any such fuction you can use and your graph looks like

PS:I would suggest you to use LaTeX to type your questions.

$\endgroup$

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy