Answer
The graph is shown below:
Work Step by Step
The constant term of the polynomial $f\left( x \right)$ is:
${{a}_{0}}=-2$
This gives the possible factors of ${{a}_{0}}$:
$p\,\,=\,\,\pm 1,\,\,\pm 2$
The leading coefficient of the polynomial $f\left( x \right)$ is:
${{a}_{n}}=4$
This gives the possible factors of ${{a}_{n}}$:
$q=\pm 1,\,\,\pm 2,\,\,\pm 4$
Therefore, using the rational zero theorem, the possible rational zeros of the functions are:
$r=\pm 1,\,\,\pm 2,\,\,\pm \frac{1}{2},\,\,\pm \frac{1}{4}$
Therefore, the rational zeros of the functions are $r=-\frac{1}{2},\,\,\frac{1}{2}$
