### Home > PC > Chapter 2 > Lesson 2.3.1 > Problem2-76

2-76.

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.

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.

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