Re: Piecewise functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg51587] Re: Piecewise functions*From*: Bill Rowe <readnewsciv at earthlink.net>*Date*: Sat, 23 Oct 2004 00:23:10 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

On 10/21/04 at 10:22 PM, luca at nospam.it (Luca) wrote: >Hi all. I'm studying for the exam of signals and systems and I was >trying to plot some kind of functions I transformed for exercise. >So, I need to plot piecewise functions like: >y(x) = x if x > 3 >y(x) = -x if -1 < x < 3 >y(x) = 1 else >(should have been a system). I found out in the guide the chapter >about this, and I learned that it is possible with the function >UnitStep, which I know. Anyway, I found it difficult to determine >the equation of the function using this method. Is it possible to >do it simply writing everything like I did before, more or less? >i.e. without having to determine the equation with the UnitStep >function. Yes, it is possible to do this. For example you could do y[x_] := x /; x > 3 y[x_] := -x /; -1 < x < 3 y[x_] := 1 /; x < -1 and Plot[y[x], {x, -2, 5}]; verifies the function y behaves as desired. But there are advantages to using Unit step For example, trying to integrate y Integrate[y[x], {x, -2, 0}] Integrate[y[x], {x, -2, 0}] simply returns the integral unevaluated. Using Unit step g[x_] := UnitStep[-x - 1] - x*(UnitStep[x + 1] - UnitStep[x - 3]) + x*UnitStep[x - 3] and then Plot[g[x], {x, -2, 5}]; show g is the same function as y now Integrate[g[x], {x, -2, 0}] 3/2 works since Mathematica knows how to deal with the UnitStep function. Note g could have been written as g[x_]:=UnitStep[-x - 1] + 2*x*UnitStep[x - 3] - x*UnitStep[x + 1] which is somewhat simpler than what I wrote above. But the way I wrote it above is easier for me to see what g does. -- To reply via email subtract one hundred and four