#### Answer

$\pm1,\pm3$

#### Work Step by Step

If $p$ is a factor of the constant term and $q$ is a factor of the leading coefficient, then the potential zeros can be gained by the possible combinations in $\frac{p}{q}$.
The given polynomial function has a constant term of $3$ and a leading coefficient of $1$.
The possible factors $p$ of the constant term and $q$ of the leading coefficient are:
$p=\pm1, \pm3$
$q=\pm1$
Thus, the possible rational roots of $f(x)$ are:
$\frac{p}{q}=\pm1,\pm3$