AP Calculus AB and BC glossary
Monotonic
A function is monotonic on an interval when it is either increasing throughout or decreasing throughout, never both. Equivalently the derivative does not change sign on that interval, which also guarantees the function is one-to-one there.
Monotonic functions are invertible on that interval, since each output comes from exactly one input. That is why inverse function questions specify an interval where the function is monotonic.
The mistake
Confusing it with bounded. A monotonic sequence may run off to infinity; monotonic and bounded together are what force convergence.
Appears in: Unit 5: Analytical Applications, Unit 10: Infinite Sequences and Series (BC)