3D Space-Function of two variables

[nalkapo]

Hello everybody,
I am studying a theorem and I want to convert a function of one variable into a function of two variables. At first steps I am really confused and don't know what to do.
Can you help me with this step:

function with one variable:
given; f(x),
f(0)=f(1)=0 on [a,b]=[0,1]

->I converted as: f(x,y),
f(0,0)=f(1,0)=0 on [a,b]x[c,d] = [0,1]x[0,1]

Is that conversion true?

 

[radou]

Well, if you define your new function as g(x, y) = f(x) + y, then it holds.

 

[nalkapo]

Well, if you define your new function as g(x, y) = f(x) + y, then it holds.

thanks radou for the answer, let me make my question more clear:
single variable function is on the interval [0,1].
if I prove this for two variables, then what the interval will be?
will it be an interval or an area like a rectengular [a,b]x[c,d]?
I thought the endpoints should be [0,1]x[0,1]. is that true?

 

[radou]

Your domain can be [0, 1] x any closed interval containing 0, if you want the function g to work this way.