Answer
The graph is shown below:
Work Step by Step
The constant term of the polynomial $f\left( x \right)$ is:
${{a}_{0}}=-4$
This gives the possible factors of ${{a}_{0}}$:
$p=1,2,4$
The coefficient of the term with the highest power of the polynomial $f\left( x \right)$ is:
${{a}_{n}}=6$
This gives the possible factors of ${{a}_{n}}$:
$q=1,2,3,6$
Therefore, using the rational zero theorem the possible rational zeros of the functions are:
$r\,\,=\,\,\pm 1,\,\,\pm 2,\,\,\pm 4,\,\,\pm \frac{1}{2},\,\,\pm \frac{2}{2},\,\,\pm \frac{4}{2},\,\,\pm \frac{1}{3},\,\,\pm \frac{2}{3},\,\,\pm \frac{4}{3},\,\,\pm \frac{1}{6},\,\,\pm \frac{2}{6},\,\,\pm \frac{4}{6}$
Therefore, the rational zeros of the functions are $r=\frac{1}{2},\,\,\frac{2}{3},\,\,2$.
