How to restrict the domain of a function

Question

I realize this question has been asked many times, but I am fairly new at Mathematica and the other answers are very complex, and certainly too complicated for this simple code I am trying to write.

I want to restrict the function below to be between -1 and 1. I do not want to restrict the plot; I want to restrict the function itself.

f[x_] := -(x + c)^2

Is there a simple way I can do this?

Is this what you are after: http://reference.wolfram.com/language/ref/Condition.html? — Kuba, Jan 15 '18 at 19:17
So far I haven't had any luck with this method. I suppose I could be doing it wrong though. — Physika, Jan 15 '18 at 19:25
Possible duplicate of Can I limit PlotRange for 1 function in a Plot? — Artes, Jan 15 '18 at 20:03

score 12 · Accepted Answer · edited Jan 16 '18 at 07:39

12

I think the easiest way is to use Condition which has the operator form /;.

f[x_ /; -1 <= x <= 1, c_] := -(x + c)^2

Then

With[{c = -1/4}, Plot[f[x, c], {x, -2, 2}]]

edited Jan 16 '18 at 07:39

Mr.Wizard

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answered Jan 15 '18 at 22:29

m_goldberg

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This worked! Thank you! – Physika Jan 15 '18 at 23:45
1

@Physika consider also reading (1835) – Mr.Wizard Jan 16 '18 at 07:40

score 4 · Answer 2 · answered Jan 16 '18 at 03:53

Amplifying on m_goldberg's answer: The Condition can include a Message to use when the argument is outside the allowed interval.

ClearAll[f]

f::arg = "Argument value of `1` must be in the closed interval {-1, 1}.";

f[x_, c_] /; If[TrueQ[-1 <= x <= 1], True, Message[f::arg, x]] := -(x + c)^2

Then, an argument outside the interval generates a Message

f[2, c]

The Message can be turned Off

With[{c = -1/4}, Off[f::arg]; Plot[f[x, c], {x, -2, 2}]]

How to restrict the domain of a function

2 Answers2

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