Find a piecewise definition of f that does not involve the absolute value function. ---

Question

Find a piecewise definition of f that does not involve the absolute value function. --->

anonymous · Answer

$$f(x)=\left| x+4 \right|$$

anonymous · Answer

square it and take square root

anonymous · Answer

$$\sqrt{(x+4)^2}$$

anonymous · Answer

i think we are over complicating it...they actually want a piecewise function this time.

anonymous · Answer

I can do this nicely in LaTeX, one second

anonymous · Answer

me too!

anonymous · Answer

$$f(x) = |x+4| = \left\{\begin{array}{c|c}
x + 4  & x \geq -4 \
- x - 4 & x < -4
\end{array}
\right.$$

anonymous · Answer

yeah thats what they were looking for.  we can one-up them though with our:
$$\sqrt{(x+4)^2}$$

anonymous · Answer

lol

anonymous · Answer

$$   f(x) = \left\{
     \begin{array}{lr}
       -x-4 & : x <-4\
        x+4 & : x \geq 4
     \end{array}
   \right.$$

zarkon · Answer

I prefer commas 

$$f(x) = |x+4| = \left\{\begin{array}{rc}
x + 4,  & x \geq -4 \
- x - 4, & x < -4
\end{array}
\right.$$

and right justifying the terms :)

anonymous · Answer

a line is nice and clean

anonymous · Answer

yeah yours is better

anonymous · Answer

$$f(x) = \left\{
     \begin{array}{lr}
       -x-4 & : x <-4\
        x+4 & : x \geq -4
     \end{array}
   \right.$$

zarkon · Answer

or 

$$f(x) = |x+4| = \left\{\begin{array}{rcc}
x + 4 & \text{if}  & x \geq -4 \
- x - 4& \text{if}  & x < -4
\end{array}
\right.$$

anonymous · Answer

Yes I've seen that format often too

anonymous · Answer

show off!