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

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

   Hint (a):

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

2. Write two equations that could represent the functions $g(x)$ and $k(x)$. Watch out for changes in the domain.

   Hint (b):

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