Answer
$\pm1,\pm\frac{1}{2}$
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 $1$ and a leading coefficient of $2$.
The possible factors $p$ of the constant term and $q$ of the leading coefficient are:
$p=\pm1$
$q=\pm1,\pm2$
Thus, the possible rational roots of $f(x)$ are:
$\frac{p}{q}=\pm1,\pm\frac{1}{2}$
