Originally Posted by
dorkymichelle Is my graph correct? How do I find the range according to the graph?
let $\displaystyle f(x) = |x+4|-1, -6 \leq x<-3$
$\displaystyle 9-x^2, -2< x \leq 1$
$\displaystyle (/sqrtx-2)+2, 2 \leq x < 6$
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.
$\displaystyle
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]: $\displaystyle f(x)=|x+4|-1 \ \ if \ \ -6 \leq x < -3$
Code:
x | f(x)
--|-----
-6| 1 Closed
-5| 0
-4| -1
-3| 0 Open
Branch [2]: $\displaystyle f(x)=9-x^2 \ \ if \ \ x \leq 1$
Code:
x | f(x)
--|-----
1 | 8 Closed
0 | 9
-1| 8
-2| 5
-3| 0 No reason to stop here!
-4| -7
Branch [3]: $\displaystyle f(x)=\sqrt{x-2}+2 \ \ if \ \ 2 \leq x<6$
Code:
x | f(x)
--|-----
2 | 2 Closed
3 | 3
6 | 4 Open