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Calculus: Early Transcendentals
Sketch the graph of the function and use it to determine the values of $ a $ for which $ \displaystyle \lim_{x\to a}f(x) $ exists.
$$ f(x) = \left\{
\begin{array}{ll}
1 + x & \mbox {if $ x < -1 $}\\
x^2 & \mbox{if $ -1 \le x < 1$}\\
2 - x & \mbox{if $ x \ge 1 $}
\end{array} \right.$$