# What is the correct term for an increasing or decreasing function which “flattens out”?

I'd like to say logarithmically decreasing but it does not have to decrease to zero.

An example of an increasing function which flattens out at around 4.5%.

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It still isn't clear what "flatten out" means precisely. Do $y=\sqrt{x}$ or $y=\log(x)$ "flatten out"? These functions have the property that they are always increasing, do not tend to a finite limit, but their rate of increase goes to $0$ as $x$ goes to infinity. –  Jonas Meyer Feb 8 '11 at 0:10
@Jonas: No, they don't "flatten out". Horizontal asymptote is exactly what I was looking for. –  Jacob Feb 8 '11 at 2:29
Thanks! Just wanted to be sure. –  Jonas Meyer Feb 8 '11 at 3:24
I don't know what "flattens out" means (and your image doesn't load), but maybe you're thinking of functions of a variable $x$ which tend monotonically to a limit as $x$ tends to infinity. Having a "horizontal asymptote" is another common related term.