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

*To*: mathgroup at smc.vnet.net*Subject*: [mg90118] Re: One thing in two ways, with different result.*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Sun, 29 Jun 2008 05:37:18 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <g451vv$pqg$1@smc.vnet.net>

damayi wrote: > 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. Depending on how you define your functions, Mathematica may or may not look for and find discontinuities points. Defining a peacewise function thanks to *Peacewise[]* is a good hint to Mathematica that it should spend some extra time looking for discontinuities. So in the case of g you can tell Plot to exclude the discontinuous point at one and get the exact same plot as for f. g[x_] := x^3 /; x <= 0 g[x_] := x /; 0 < x <= 1 g[x_] := Sin[x] /; x > 1 f[x_] := Piecewise[{{x^3, x <= 0}, {x, 0 < x <= 1}, {Sin[x], x > 1}}] Plot[g[x], {x, -2, 3}, Exclusions -> 1] Plot[f[x], {x, -2, 3}] Regards, -- Jean-Marc