Originally Posted by
dorkymichelle 
Is my graph correct? How do I find the range according to the graph?
let
 = |x+4|-1, -6 \leq x<-3)
+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.
![<br />
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}](http://latex.codecogs.com/png.latex?<br />
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]: =|x+4|-1 \ \ if \ \ -6 \leq x < -3)
Code:
x | f(x)
--|-----
-6| 1 Closed
-5| 0
-4| -1
-3| 0 Open
Branch [2]: =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]: =\sqrt{x-2}+2 \ \ if \ \ 2 \leq x<6)
Code:
x | f(x)
--|-----
2 | 2 Closed
3 | 3
6 | 4 Open
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