Claim in a Differential Topology lecture:
Consider the collection $G$ of maps from $\mathbb R→\mathbb R^2$ which intersect the $x$ axis transversally at a single point. Then $G$ is a stable class.
My Problem: Choose a curve that passes through origin, and perturbe it so that it becomes graph of $x^3$ so since $x^3$ doesnot intersect transversally with $x$ axis, so is not $G$ unstable class?