# Piece wise function graphs

• Dec 13th 2009, 03:27 PM
dorkymichelle
Piece wise function graphs
Is my graph correct? How do I find the range according to the graph?
let $f(x) = |x+4|-1, -6 \leq x<-3$
$9-x^2, -2< x \leq 1$
$(/sqrtx-2)+2, 2 \leq x < 6$
• Dec 14th 2009, 01:17 PM
masters
Quote:

Originally Posted by dorkymichelle
Is my graph correct? How do I find the range according to the graph?
let $f(x) = |x+4|-1, -6 \leq x<-3$
$9-x^2, -2< x \leq 1$
$(/sqrtx-2)+2, 2 \leq x < 6$

Hi dorkymichelle,

Well, I don't get what you got. I don't have a graphing program where I can show you, but here are the three functions and tables. Graph them and see the differences.

$
f(x)=\begin{cases}[1] \ \ |x+4|-1, & \text{ if }-6 \leq x <-3 \\ [2] \ \ 9-x^2, & \text{ if }x \leq 1 \\ [3] \ \ \sqrt{x-2}+2, & \text{ if } 2\leq x < 6 \end{cases}$

Branch [1]: $f(x)=|x+4|-1 \ \ if \ \ -6 \leq x < -3$
Code:

x | f(x) --|----- -6| 1  Closed -5| 0 -4| -1 -3| 0  Open
Branch [2]: $f(x)=9-x^2 \ \ if \ \ x \leq 1$

Code:

x | f(x) --|----- 1 | 8  Closed 0 | 9  -1| 8 -2| 5 -3| 0 No reason to stop here! -4| -7
Branch [3]: $f(x)=\sqrt{x-2}+2 \ \ if \ \ 2 \leq x<6$

Code:

x | f(x) --|----- 2 | 2  Closed 3 | 3 6 | 4  Open