monotonically increasing function
nounUK /ˌmɒnəˈtɒnɪkli ɪnˈkriːsɪŋ ˈfʌŋkʃən/
US /ˌmɑːnəˈtɑːnɪkli ɪnˈkriːsɪŋ ˈfʌŋkʃən/
A function that never goes down as you move to the right.
The function f(x) = 2x is monotonically increasing because bigger inputs always give bigger outputs.
SYNONYMS
OTHER MEANINGS
2. A function whose output never decreases, though it may stay flat between points.
The step function that stays at 1 and then jumps to 2 is monotonically increasing.
3. A function where x1 < x2 always implies f(x1) ≤ f(x2).
We proved the sequence is monotonically increasing by checking each consecutive pair.
4. In some texts, a strictly increasing function where x1 < x2 implies f(x1) < f(x2).
Some authors call f(x) = x³ monotonically increasing in the strict sense.