Consider the following.

$f(x)=\{\begin{array}{ccc}{e}^x& if& x<mn>1</mn>\\ x^2& if& x1\\ a=1\end{array}$

Find the left$-$hand and right$-$hand limits at the given value of $a.$

$\underset{x{1}^{-}}{lim}f(x)=$

$\underset{x{1}^{+}}{lim}f(x)=$

Explain why the function is discontinuous at the given number $a.$

Since these limits are $-$Select$--\underset{x1}{lim}f(x)$ and $f$ is therefore discontinuous at $1.$

Sketch the graph of the function.