12.4 Exercise 95

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 limit as $x$ approaches $a ,$ state it. If not, discuss why there is no limit.

$f \left(x\right) = \left\{\right. \begin{matrix}\left|x\right| - 1 , & i f & x \neq 1 \\ x^{3} , & i f & x = 1\end{matrix} \textrm{ }\textrm{ } a = 1$