Piecewise function

Questions
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1

Dear friends

I need to define and plot a 6-piecewise function but the software only accept 3 and when i try to add more, the font color changes to red and the program does not execute. Can anyone help me?
All the best

2

Try defining a 2-part piecewise function, each piece itself being a 3-part piecewise function. Or, alternatively, 3 then 2.

3

The region specifications are a list of lists. You forgot the outer brackets.

Best, David

(* this *)
Piecewise[{0, x < 1}, {1, x < 2}, {3, x < 3}, {4, x < 4}, {5, True}]

(* should be this *)
Piecewise[{{0, x < 1}, {1, x < 2}, {3, x < 3}, {4, x < 4}, {5, True}}]
4

Thanks to Blinder and David

Via your instructions, I plotted the 6-piecewise function (Blue) and a 6th order polynomial function (Pink) at the same time. but the piecewise function has a discontinuity at x=-2 and a bit right while it shouldn’t be like that since it is a 3rd order polynomial!!! Any reason?

NewPlot.jpg
NewPlot.jpg667Ă—413 16.8 KB

Enclosed find the code. Any comment will be welcome.

5

Hi Philip,

I see the same thing. It can be eliminated by increasing the number of points plotted. But I do think it would be better if Plot knew to plot to the endpoints of segments.

Plot[{Piecewise[{{0.6 - 0.3692*(x + 3) - 0.0308*(x + 3)^3, -3 < 
      x <= -2}, {0.2 - 0.46154*(x + 2) - 0.0923*(x + 2)^2 + 
      0.95385*(x + 2)^3, -2 < x <= -1}, {0.6 + 2.2154*(x + 1) + 
      2.7692*(x + 1)^2 - 2.5846*(x + 1)^3, -1 < x <= 0}, {3 - 
      4.9846*x^2 + 2.58462*x^3, 
     0 < x <= 1}, {0.6 - 2.21538*(x - 1) + 2.76923*(x - 1)^2 - 
      0.95384*(x - 1)^3, 
     1 < x <= 2}, {0.2 + 0.46154*(x - 2) - 0.0923*(x - 2)^2 + 
      0.0308*(x - 2)^3, 2 < x <= 3}}], 
  3 - 3.20667*x^2 + 0.866667*x^4 - 0.06*x^6}, {x, -3, 3}, 
 PlotPoints -> 1000]