12.4 Exercise 137

With the use of a graphing utility, use numerical or graphical evidence to determine the left- and right-hand limits of the function given as $x$ approaches $a .$ If the function has a limit as $x$ approaches $a ,$ state it. If not, discuss why there is no limit

$f \left(x\right) = \left\{\right. \begin{matrix}\frac{1}{x} - 3 , \textrm{ }\text{i} f & x \leq 2 \\ x^{3} + 1 , i f & x > 2\end{matrix} \textrm{ }\textrm{ } a = 2$