Sketch $f(x) = \left\{ \begin{array} { c l } { - 2 x + 7 } & { \text { for } x < 3 } \\ { 2 x - 5 } & { \text { for } x \geq 3 } \end{array} \right.$. 

1. This graph should look like a function you have seen before, that is, the absolute value function. Write an equation for $f(x)$ using the absolute value function with the necessary transformations.

   Hint (a):

   The general absolute value function is $y = a\left|x − h\right| + k$, where $(h, k)$ is the vertex and a is the steepness of the two lines.

2. Shift $y = f(x)$ to the left $5$ units and down $3$ units. Write the new equation, $g(x)$, as an absolute value function.

   Hint (b):

   This is $f(x + 5) − 3$.
   Change the domain for the horizontal shift only.

3. Now write an equation for $g(x)$ using a piecewise-defined function. (Verify your solution by using a graphing calculator.) Compare this equation to the original equation for $f(x)$. What do you notice?