dg.differential geometry - Differentiable function germs on differentiable manifolds

Hello everyone, I was wondering if anyone knew how to prove that the map from $C^{infty}(M)$ to $xi (p)$, that is, from the infinitely differentiable functions on a manifold M to the space of (once)-differentiable function germs, where the map is associating to each f in $C^{infty}(M)$ its class in $xi (p)$ is onto.
By the way, since you ask, the reason I'm interested in this is because its a question that WAS on my final for differential topology, I've tried to work it out since then but no luck so far, this is not homework it's just curiosity now, hope its ok ill have to check the post regultaions, sorry, if not just tell me and i'll delete the question...

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