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4-123.

​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.

$y=g(x)$ 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.

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