Re: Plotting discontinuities using Exclusions
- To: mathgroup at smc.vnet.net
- Subject: [mg122762] Re: Plotting discontinuities using Exclusions
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Thu, 10 Nov 2011 06:50:33 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201111091125.GAA11166@smc.vnet.net>
- Reply-to: drmajorbob at yahoo.com
f = (x^2 - 2 x)/(x - 2); label = ToString@Factor@Numerator@f/ToString@Denominator@f; Plot[f, {x, 0, 4}, PlotLabel -> label, Exclusions -> Reduce[Denominator[f] == 0, x]] Bobby On Wed, 09 Nov 2011 05:25:48 -0600, John Accardi <johnaccardi at comcast.net> wrote: > Goal: Display the definition of a rational function in factored form > to better see points of discontinuities, like holes and then plot > the function showing the hole. > > Example 1: > > The following does the graph correctly, showing a gap at x = 2 but > requires an undesirable function definition (I want to specify > the numerator factored). > > f = (x^2 - 2 x)/(x - 2) > > (-2 x + x^2)/(-2 + x) > > Plot[f, {x, 0, 4}, Exclusions -> Reduce[Denominator[f] == 0, x]] > > > Example 2: > > More desirable is to show the function with numerator factored so > students can see the zero of the bottom being the same as the zero > in the top for the hole. For example, the following shows the function > definition > as desired but the graph then does not show the gap for the hole: > > f = x (x - 2)/(x - 2) > > x > > Plot[f, {x, 0, 4}, Exclusions -> Reduce[Denominator[f] == 0, x]] > > I suspect that Mathematica does the cancellation (outputting x) and > therefore > loses sight of the discontinuity for the plot. > > Question: > > How can I use the function definition of Example 2 and the plot output > of Example 1 in one sequence? (I want to prevent the simplification > Mathematica does when processing the function definition.) > > Thanks for any insights. > -- DrMajorBob at yahoo.com
- References:
- Plotting discontinuities using Exclusions
- From: John Accardi <johnaccardi@comcast.net>
- Plotting discontinuities using Exclusions