Sketch the graph of the following function and use it to determine the following limits. If a limit does not exist, type DNE. $$f(x) = \begin{cases} x-2, &\text{for } x \le -1 \\ x^2+3, &\text{for } -1 < x \le 1 \\ 5-x, &\text{for } x > 1 \end{cases}$$

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1. $\displaystyle \lim_{x \to -1^{-}}f(x) =$

2. $\displaystyle \lim_{x \to -1^{+}}f(x) =$

3. $\displaystyle \lim_{x \to -1}f(x) =$

4. $\displaystyle \lim_{x \to 1}f(x) =$

5. $\displaystyle f(-1) =$

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