TITLE: Is every virtually free group residually finite?
QUESTION [7 upvotes]: Question: Is every (finitely generated) virtually free group residually finite?
A well-known question asks whether every hyperbolic group is residually finite (Mladen Bestvina. Questions in geometric group theory. http://www.math.utah.edu/ ~bestvina/eprints/questions- updated.pdf.). My question is a very speciall case, and I wonder if it has been done.
It is known that residual finiteness is not a quasi isometry invariant (Is residual finiteness a quasi isometry invariant for f.g. groups?).

REPLY [2 votes]: To add to the list, here's a proof that is probably actually longer than the others, but is immediate "modulo standard facts".
Standard fact 1: All finitely generated free groups embed into $SL_2(\mathbb{Z})$. Indeed, famously the congruence subgroup $\Gamma(2)$ of $PSL_2(\mathbb{Z})$ is free of rank 2, all finitely generated free groups embed in $F_2$, and by the universal property we can embed into $SL_2(\mathbb{Z})$.
Standard fact 2: $SL_2(\mathbb{Z})$ is residually finite. Indeed, given a non-identity matrix, map to $SL_2(\mathbb{Z}/n)$ for large enough $n$.