Cubic function that has no y intercept

Question

Is there a cubic function that is only in quadrants 1 and 2 of the coordinate plane and so never crosses the y axis? If so can you give me a cubic function that does that?

Answer 1

For a function to not have a $y$-intercept, the number $0$ would have to not be in its domain. $0$ is the the domain of every polynomial, including every cubic function, so they all have $y$-intercepts.

Answer 2

Do you mean a polynomial $P(x,y)$ of total degree $3$ such that the curve $P(x,y) = 0$ is only in one half-plane? For example, $x y^2 + x - 1 = 0$ is only in the first and fourth quadrants, while $ x^2 y + y - 1$ is only in the first and second.