Proving linearity of a planar function

[rem45]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

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

 

[LCKurtz]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

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

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.

 

[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!