Answer
The graph is shown below:
Work Step by Step
The constant term of the polynomial $f\left( x \right)$ is:
${{a}_{0}}=15$
This gives the possible factors of ${{a}_{0}}$ which are:
$p=1,3,5,15$
The coefficient of term with highest power of the polynomial $f\left( x \right)$ is:
${{a}_{n}}=2$
This gives the possible factors of ${{a}_{n}}$ which are:
$q=1,2$
Therefore, using the rational zero theorem, the possible rational zeros of the function are:
$r=\pm 1,\pm 3,\pm 5,\pm 15,\pm \frac{1}{2},\pm \frac{3}{2},\pm \frac{5}{2},\pm \frac{15}{2}$
Therefore, the rational zeros of the function are $r=-\frac{1}{2},3,5$.
