Re: One thing in two ways, with different result.

*To*: mathgroup at smc.vnet.net*Subject*: [mg90119] Re: [mg90099] One thing in two ways, with different result.*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sun, 29 Jun 2008 05:37:29 -0400 (EDT)*Reply-to*: hanlonr at cox.net

Piecewise automatically excluded the discontinuity. Without Piecewise you need to explicitly exclude it from the Plot using the option Exclusions. f[x_] := Piecewise[{{x^3, x <= 0}, {x, 0 < x <= 1}, {Sin[x], x > 1}}] g[x_] := x^3 /; x <= 0 g[x_] := x /; 0 < x <= 1 g[x_] := Sin[x] /; x > 1 Plot[f[x], {x, -1, 2}] Plot[g[x], {x, -1, 2}, Exclusions -> 1] Bob Hanlon ---- damayi <damayi at gmail.com> wrote: > Dear all, > Today I encountered a confused question, and I hope you can help me. > I defined a function g[x] in the following and Plot it. > g[x_] := x^3 /; x <= 0 > g[x_] := x /; 0 < x <= 1 > g[x_] := Sin[x] /; x > 1 > > Then I defined another function f[x] that is the same as g[x] in my > opinion, and Plot it. > f[x_] := Piecewise[{{x^3, x <= 0}, {x, 0 < x <= 1}, {Sin[x], x > 1}}] > > You will find that Plot[g[x],{x,-2,3}] is different with Plot[f[x], > {x,-2,3] when x is 1.0 > > Since g[x] and f[x] are identify, why are these plot different ? > By the way, my Mathematica is 6.0.2. > > Best Regards > mayi > 2008-6-27 >