Guessing plot of two-variable function

[twoflower]

Hi all,

recently we've been practising drawing a plot of two-variables functions (we're currently doing metric spaces).

Well, I don't know how to guess the plot for let's say:
$$f(x, y) = \sqrt{x^2 + y^2}$$

One guy came to the blackboard and drew it quite quickly

Thank you for the suggestions.

 

[Physics Monkey]

Some things you can see right away. The function is always positive. It depends only on $$x^2 + y^2$$ and is thus symmetric between x and y. The function is an increasing function of x and y. Basically this function is the distance from the origin to the point (x,y) and therefore its level curves are circles.

In general, look for symmetry, positivity, maxima, zeros, behavior at infinity, level curves, and anything you can easily identify (I'm not saying it is always easy to just see the level curves, max/min, etc but in this case it is).

Does that help?