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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



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