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This question already has an answer here:

For Plot[x^12 - x^9 + x^4 + 1, {x, -.001, .001}] enter image description here

Details on Y-axis seem to be wrong.I am using V 9.0.1.0 .Bug?

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marked as duplicate by Jason B., Kuba, Michael E2 plotting Nov 30 '15 at 11:04

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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This function is set up so that the relative difference between the values is tiny. Just look at the average value of the function over the range, versus the variation,

Differences@(Function[x, x^12 - x^9 + x^4 + 1] /@ {.001, 0.005, 0.0})
Mean@(Function[x, x^12 - x^9 + x^4 + 1] /@ {.001, 0.005, 0.0})
(* {6.24*10^-10, -6.25*10^-10} *)
(* 1. *)

Even scientific notation isn't going to save you here since you need a large number of digits to see the differences. So just adapt this answer to suit your problem,

ticks[min_, max_] := {#, NumberForm[#, {20, 15}]} & /@ 
  N[FindDivisions[{min, max}, 5]]

Plot[(x^12 - x^9 + x^4 + 1), {x, -.001, .001}, 
 Ticks -> {Automatic, ticks}]

enter image description here

Or better yet, something like this,

Plot[(x^12 - x^9 + x^4 + 1) - 1, {x, -.001, .001}, Axes -> False, 
 Frame -> True, FrameLabel -> {"x", "f(x)-1"}]

enter image description here

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