Y proportional to the inverse of X
Y proportional to the inverse of X is a common form of equations in physics and a curved graph like this will show the connection between the two. For example from the wave equation velocity = frequency x wavelength (V=fλ) then f is proportional to 1/λ. Since X can be either positive or negative Y can also be positive or negative
Y proportional to X squared
The connection Y proportional to X squared is another common connection in physics equations. For example Kinetic energy = 1/2 mass x velocity squared (KE= 1/2mv2) and Einsteins famous equation E=mc2
Y will be always be positive even when X is negative because the square of a negative number is positive.
Y proportional to root X
Y proportional or equal to the square root of X also written Y = √X and Y = X1/2
Equations of this form are also common in physics, for example, velocity is proportional to the square root of kinetic energy √2 KE/m = v
Since it is not possible to have a negative value of a square root both X and Y are always positive.