### Home > PC > Chapter 2 > Lesson 2.1.2 > Problem2-23

2-23.

Sketch $f(x) = \left\{ \begin{array} { c l } { - 2 x + 7 } & { \text { for } x < 3 } \\ { 2 x - 5 } & { \text { for } x \geq 3 } \end{array} \right.$. 2-23 HW eTool (Desmos)

Graph two lines. Sketch the first one to the right of $x = 3$, the second one to the left of $x = 3$.

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

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 $f\left(x\right)$ to the left five units and down three units. Write the new function, $g(x)$, as an absolute value function.

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

3. Verify your solution by using a graphing calculator.

Use the eTool below to view the graphs.
Click the link at right for the full version of the eTool:
2-23 HW eTool (Desmos)