# Thread: Split/Piece Wise Functions with absolute values

1. ## Split/Piece Wise Functions with absolute values

In my calculus class, we are going over these as a review, but I have completely forgotten how to do them and the teacher didn't really explain them since he assumed we knew them.

We are supposed to make several functions into split functions.

Y=5-|2x-10| and Y=2x^2-|x^2-9|

I have completely forgotten how to do these so if anybody could explain them that'd be great. I have to get these quickly.

2. Originally Posted by lawlerskates
In my calculus class, we are going over these as a review, but I have completely forgotten how to do them and the teacher didn't really explain them since he assumed we knew them.

We are supposed to make several functions into split functions.

Y=5-|2x-10| and Y=2x^2-|x^2-9|

I have completely forgotten how to do these so if anybody could explain them that'd be great. I have to get these quickly.
do you remember how we define absolute values?

recall that $|x| = \left \{ \begin{array}{lr} x & \mbox{ if } x \ge 0 \\ & \\ -x & \mbox{ if } x < 0 \end{array} \right.$

does that help?

Hint: of course, you are not just dealing with x here, but functions. the same rule applies. you can replace x with f(x) in the above definition as well

3. Yea I remember that, but I'm really just blanking out on these ones.

For the 5-|2x-10|, when I split them, do I make the first one 5-(2x-10) and the second 5+(2x+10)?

4. Originally Posted by lawlerskates
Yea I remember that, but I'm really just blanking out on these ones.

For the 5-|2x-10|, when I split them, do I make the first one 5-(2x-10) and the second 5+(2x+10)?
nope

going strictly by the definition:

$5 - |2x - 10| = \left \{ \begin{array}{lr} 5 - (2x - 10) & \mbox{ if } 2x - 10 \ge 0 \\ & \\ 5 - [ -(2x - 10)] & \mbox{ if } 2x - 10 < 0 \end{array} \right.$

now just simplify things (including the ranges)

5. Alright I'm finally starting to get it again. Thanks a lot.