If the graph of the function $y=f\left(x\right)$ is

and the graph of the function $y=g\left(x\right)$ is

Then discuss the continuity of $f\left(x\right) g\left(x\right)$ at $x=3$ and $x=2.$

Find the interval for which the function given by the following expression is continuous:

 $f\left(x\right)=\frac{3x+7}{x^2-5x+6}$.

Find the interval for which the function given by the following expression is continuous:

$f\left(x\right)=\frac{\sqrt{x^2+1}}{1+{\sin }^{2}x}$.

Find the interval for which the function given by the following expression is continuous:

$f\left(x\right)=\tan \left(\frac{\mathrm{\pi }x}{2}\right)$