#### Answer

$\pm 1, \pm 7, \pm\frac{1}{2}, \pm\frac{1}{4}, \pm\frac{7}{2}, \pm\frac{7}{4}$

#### Work Step by Step

RECALL:
The possible rational zeros of a polynomial function is given by $\dfrac{p}{q}$ where:
$p$ = factor of the constant term
$q$ = factor of the leading coefficient
The given polynomial function has:
constant term = $-7$
leading coefficient = $4$
The factors of the constant term are: $\pm1, \pm7$
The factors of the leading coefficient are: $\pm 1, \pm2, \pm4$
Thus, the possible rational zeros of the given polynomial function are:
$=\pm 1, \pm 7, \pm\frac{1}{2}, \pm\frac{1}{4}, \pm\frac{7}{2}, \pm\frac{7}{4}$