Plotting discontinuities using Exclusions

*To*: mathgroup at smc.vnet.net*Subject*: [mg122748] Plotting discontinuities using Exclusions*From*: John Accardi <johnaccardi at comcast.net>*Date*: Wed, 9 Nov 2011 06:25:48 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

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.

**Follow-Ups**:**Re: Plotting discontinuities using Exclusions***From:*DrMajorBob <btreat1@austin.rr.com>