# Finding ranges of peacewise functions

• Dec 19th 2012, 11:04 AM
mimur
Finding ranges of peacewise functions
-4 if -3 < x <= 2
2x-1 if 2 < x < 4
-1/3x+2 if 4 <= x < 7

I know domain is (-3,7)
But how do you find range?

I was looking around the site and there was something about a symbol shaped like U ? I'm not sure what it is, can someone explain to me?
• Dec 19th 2012, 11:28 AM
HallsofIvy
Re: Finding ranges of peacewise functions
The "symbol shaped like U" is the set union: \$\displaystyle A\cup B\$ is the set of all members of both sets A and B. It is, simply, a way of combining various parts of an answer. I am surprised that you had not learned that long before taking pre-calculus. And, by the way, the term is "piece-wise", not "peace-wise".

For -3< x<= 2, f(x)= -4 (you don't mention a function "f" but without one what you have written makes no sense at all) so one possible value for f(x) is -4.
For 2< x< 4, f(x)= 2x- 4 so that f(x) can take on values between 2(2)- 4= 0 and 2(4)- 4= 4 so f(x) can take on all values of x from 0 to 4.
For 4<= x< 7, f(x)= -(1/3)x+ 2 (you wrote "-1/3x+2" which most people would interpret as -1/(3x)+ 4, but I doubt that you mean that) so f(x) can take on all values between -(1/3)(4)+ 2= -4/2+ 6/3= 2/3 and -(1/3)(7)+ 2= -7/3+ 6/3= -1/3.

The domain of the entire function is the "union" of those three sets of number.
• Dec 19th 2012, 11:58 AM
mimur
Re: Finding ranges of peacewise functions
Ah, thank you, thank you! I finally get it. I hope. Well, at least I think I do.

And yeah, I'm surprised myself. I actually transferred schools last month and I realized that my old pre-calc class didn't learn a lot of things that seemed like common knowledge to my new class (limits? What limits?).

And the piece-wise/peace-wise thing... well I did always wonder why it was called 'peace'. My old teacher had also always spelled it out like that. Man, that's kind of embarrassing. And I'm a little annoyed at her now...