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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?

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2 Answers 2

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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}]]

plot

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  • $\begingroup$ This worked! Thank you! $\endgroup$
    – Physika
    Jan 15, 2018 at 23:45
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    $\begingroup$ @Physika consider also reading (1835) $\endgroup$
    – Mr.Wizard
    Jan 16, 2018 at 7:40
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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]

enter image description here

The Message can be turned Off

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

enter image description here

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