Homework Help: Proving linearity of a planar function

1. Aug 24, 2014

rem45

1. The problem statement, all variables and given/known data

Prove or disprove the linearity of the following function
y(x)=(z^2)x(z)

2. Relevant equations

I know how to determine linearity of functions in a 2-d plane but not in 3 dimensions.

3. The attempt at a solution

How can one attempt to plot this function by making a table for x,y, and z variables?

2. Aug 24, 2014

LCKurtz

You need to tell us what are the dependent and independent variables. And explain your notation. Does y(x) mean y is a function of x? And x(z) means x is an unknown function of z?

And if it represents anything, it would be some kind of surface, which you would not normally try to draw by making a table of values.

3. Aug 24, 2014

rem45

Unfortunately that is all that is given with no other information. My mind is blown as to how to solve this. My initial approach was to create a table / convert this form to the standard ax+by+cz=d.

I am under the impression that y(x) does mean y is a function of x and similarly with x(z). Plotting this does yeild a flat plane but to put in standard form I would need a vector normal to the plane and a point on the plane neither of which I can deduce from the given information.

Any thoughts on this problem will be greatly appreciated!