High School I want to define a function knowing only it's limits

[maxhersch]

This is a random problem I am trying to figure out. The context doesn't matter.

I wish to define a function z(x, y) based on the following limits:

1. lim z (x→∞) = 0
2. lim z (x→0) = y
3. lim z (y→∞) = ∞
4. lim z (y→0) = 0

 

[kuruman]

$z(x,y)=ye^{-x}$? Can you think of another one?

 

[mathman]

$z=\frac{y}{1+x}$.

 

[mfb]

$z=\frac{y}{1+x}$.

For $x<-1$ this doesn't have the right behavior for $y \to \infty$. If we require x,y to be non-negative it works.

 

[mathman]

$z=\frac{y}{1+x^2}$