 Solution

Exactly $a\ne 0$ works. For nonzero $a$, composition with $x\mapsto ax$ preserves smoothness, and the support of a function is $[-1/|a|,1/|a|]$, which is compact. For $a=0$ the result is the strictly positive constant $\varphi (0)$ on all of $\mathbb{R}$, so it lacks compact support and is not a test function.