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Proving linearity of a planar function

  1. Aug 24, 2014 #1
    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. jcsd
  3. Aug 24, 2014 #2

    LCKurtz

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    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.
     
  4. Aug 24, 2014 #3
    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!
     
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