Sketching Multiple Variables: How to Represent 3-Dimensional Surfaces?

[stau40]

Homework Statement

Two separate problems:
1. Sketch f(x,y)=x+(y^2)
2. Sketch f(x,y)=sq rt (4-(x^2)-(y^2))

Homework Equations

The Attempt at a Solution

I honestly don't even know where to begin with sketching these two equations. In the first problem I can't find an example without a real number in the equation (all examples are similar to z=9-x^2-y^2) so I'm not sure how to begin. In the second example I realize the numbers in the sq rt need to be >=0, but I'm still not sure how to proceed and the most examples only show domain sketching. Any help would be greatly appreciated!

 

[epenguin]

The specific examples are mathematical, the general problem of how best to represent a 3-dimensional surface is maybe artistic.

You can do it by a series of slices thro the surface, e.g. slices of constant y. You seem to know how to do it for one y, e.g. y=0, y = something else and y = a few other numbers. Get what are the systematic trends.

You could also do it for a series of constant x and get a sort of net in a shape. Maybe put dots for where two curves are actually crossing to avoid confusing the eye.