In analysis, we often compute lower and upper estimates for a quantity. Sometimes these are called lower (or upper) bounds, but that seems incorrect, as a bound in analysis refers to a constant.
Calling them estimates is misleading as well: The significance of a lower "estimate" is not that it approximates the quantity (it may be very far off!), only that it is always less than the quantity, a property which "estimates" do not have.
What is the correct term, then, for non-constant lower (or upper) estimates/bounds?
You can say the quantity of interest is bounded above (resp. below) by the function $f(x),$ for example.