programming - Keep function range as a variable

Plot[2*x^2 - x + 2, {x, -1, 1}] plots a function of x from -1 to 1. As far as I can see, I cannot "save" this range in a variable:

u = {x, -1, 1};
Plot[2*x^2 - x + 2, u]

Generates Plot::pllim: Range specification u is not of the form {x, xmin, xmax}. Hopefully my intention is obvious, what is the most concise way of accomplishing it?

Because someone will wonder why I could possibly want to do this: I have

NDSolve[..., ..., {t, 0, 100}];

Plot[..., {t, 0, 100}];

I don't want to need to modify both 100's as my desired range changes. Yes, I could use variables t0 and t1, but is what type is the range/domain expression? Why can't I store it directly?

Answer

Better methods

My original answer was pretty poor and I'll show you why.

Suppose x has a value assigned: x = 7. This does not bother Plot:

Plot[2*x^2 - x + 2, {x, -1, 1}]  (* outputs graphic *)

It however will prevent my earlier suggestions from working:

Plot[2*x^2 - x + 2, Evaluate@u]

During evaluation of In[23]:= Plot::itraw: Raw object 7 cannot be used as an iterator. >>

Plot[2 x^2 - x + 2, {7, -1, 1}]

Instead you should store your range in a way that holds the plot parameter unevaluated:

u = Hold[{x, -1, 1}];

Then you need a way to put this inside the Plot expression without it evaluating. This can be done with a Function and a hold attribute and Apply:

Function[spec, Plot[2*x^2 - x + 2, spec], HoldAll] @@ u  (* outputs graphic *)

Or more tersely with the "injector pattern":

u /. _[spec_] :> Plot[2*x^2 - x + 2, spec]  (* outputs graphic *)

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Old answer

You just need Evaluate:

u = {x, -1, 1};


Plot[2*x^2 - x + 2, Evaluate @ u]

Or as I often prefer, Function:

Plot[2*x^2 - x + 2, #] & @ u