The normal way to change the display range of an axis is:

histogram->GetYaxis()->SetRangeUser(lower,upper);

but there are several situations where this fails. See below for help in these cases.

Assume you have a histogram which has been normalized it with

hist->SetNormFactor(1)

Your Y-axis will show values between 0 and 1. Trying to set the Y range using these values, eg.

SetRangeUser(0.01, 0.2)

will fail however. You still need to give the range in the original unnormalized units.

You can scale normalized units back with:

Double_t scaleY = hist->GetEntries()/hist->GetNormFactor();
hist->GetYaxis()->SetRangeUser(normalizedLower*scaleY,normalizedUppe*scaleY);

Do not try to SetLimits or SetRangeUser of any histogram. Instead use the following code:

THStack *hs = new THStack("hs","test stacked histograms");
hs->SetMinimum(0.);
hs->SetMaximum(10.);

If you have a TGraph, SetRangeUser will not work for the x axis. It will not complain but also not do anything. Or not the thing you want.

You have to use SetLimits(), like:

TGraph* myGraph = new TGraph();
...
myGraph->GetXaxis()->SetLimits(lower,upper);