Does this map define a rational map?

Question

$\phi(x,y)=\frac{y-x^2}{x^2}$ for $\phi:X\to\mathbb{A}^1(\mathbb{C})$

$X$ being a variety $X=V(\langle x^5-x^4+2x^2y-y^2\rangle) \subset \mathbb{A}^2(\mathbb{C})$

Answer 1

A rational map is an equivalence class of maps defined on open subsets of $X$. The map you defined above is defined on the open subset of $X \subseteq \mathbb A^2(\mathbb C)$ where $x \neq 0$, so it represents a rational map.

Hope that helps,