  ### Home > APCALC > Chapter 2 > Lesson 2.2.1 > Problem2-50

2-50.

Consider the functions $f(x)=\log(3-x)$ and $g(x) = \sqrt {x-3} -2$.

1. What is the domain of each function?

Recall that domains of the parent functions:

$\text{Domain of }y = \text{log}(x)\text{ is } x> 0$

$\text{Domain of }y = \sqrt{x}\text{ is } x\geq 0$

The domain will shift with the function.

2. Graph $h ( x ) = \left\{ \begin{array} { l l } { \operatorname { log } ( 3 - x ) } & { \text { for } x < 3 } \\ { \sqrt { x - 3 } - 2 } & { \text { for } x \geq 3 } \end{array} \right.$ on your graphing calculator.

3. Explain why $h$ is not continuous at $x = 3$.

Consider: $x \rightarrow 3^−, y \rightarrow$ _________ and $x \rightarrow 3^+, y \rightarrow$ ________
Do the left and the right approach the same value?

4. What is the range of each function?

Consider the range of each piece of the piecewise function separately.

Use the eTool below to view the graphs for part (b).
Click on the link to the right to view the full version of the eTool. Calc 2-50 HW eTool