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Graph the following piecewise-defined functions.
$\displaystyle{g(x) = \left\{ \begin{array}{ccc} 2 &\textrm{for}& x \lt 1\\ 1 + \sqrt{x} &\textrm{for}& x \ge 1 \end{array}\right. }$
$\displaystyle{f(x) = \left\{ \begin{array}{ccc} x^2 + 1 &\textrm{for}& x \lt 2\\ 5 &\textrm{for}& 2 \le x \le 4\\ 2x-5 &\textrm{for}& x \gt 4 \end{array}\right.}$
$\displaystyle{f(x) = \left\{ \begin{array}{ccc} -1 &\textrm{if}& x \lt 0\\ 0 &\textrm{if}& x = 0\\ 1 &\textrm{if}& x > 0 \end{array}\right.}$
$\displaystyle{f(x) = \left\{ \begin{array}{ccc} 3 &\textrm{if}& x \le -2\\ x^2 - 1 &\textrm{if}& -2 \lt x \le 3\\ -\sqrt{25-x^2} &\textrm{if}& x \gt 3 \end{array}\right.}$
$\displaystyle{f(x) = \left\{ \begin{array}{ccc} -4x &,& x \le -1\\ \sqrt{1-x^2} &,& -1 \lt x \lt 1\\ -2 &,& x \ge 1 \end{array}\right.}$
$\displaystyle{g(x) = \left\{ \begin{array}{ccc} 4-x^2 &,& x \lt -1\\ -2 &,& x = -1\\ \sqrt{4-x^2} &,& x \gt -1 \end{array}\right.}$