​Let $f(x) = \left\{ \begin{array} { c c c } { x ^ { 2 } } & { \text { for } } & { x < 2 } \\ { 4 } & { \text { for } } & { x \geq 2 } \end{array} \right.$. 

1. Let $g(x)=f(x)+2$ and $k(x)=f(x-3)$. Sketch the graphs of $y=f(x)$, $y=g(x)$, and $y=k(x)$ on the same set of axes. Use contrasting colors and label the graphs.

   Hint (a):

   1. $y=g(x)$ and $y=k(x)$ are each shifts of $y=f(x)$.

2. Write explicit equations to represent the functions $g$ and $k$. Be sure to change the domain of $f$ when writing these equations.

   Hint (b):

   Shifting the function horizontally changes the domain. Shifting the function vertically does not.