Isso is right! There's a few post on the forum that explain how to limit the range. You should make a quick search !
And I suggest you to get familiar with SIGNAL/SLOT since Qt is based on those.
For example, you could just create your own class that inherit from QCustomPlot, and create a function like :
void YourOwnClass::setRange(QCPRange range){
for(int i=0; i<this->axisRects().size(); i++ ){
if(range.lower<0)
this->axisRect(i)->axis(QCPAxis::atBottom)->setRange (0,range.upper);
else
this->axisRect(i)->axis(QCPAxis::atBottom)->setRange(range);
}
}
and connect the SIGNAL "rangeChanged" of your axis to this SLOT(function). In this case, the axis won't go below 0.