What is "increasing function"

Increase \In*crease"\, v. i. [imp. & p. p. Increased; p. pr. & vb. n. Increasing.] [OE. incresen, encresen, enrescen, OF. encreistre, fr. L. increscere; pref. in- in + crescere to grow. See Crescent, and cf. Decrease.]

1. To become greater or more in size, quantity, number, degree, value, intensity, power, authority, reputation, wealth; to grow; to augment; to advance; -- opposed to decrease.

   The waters increased and bare up the ark.
   --Gen. vii. 17.

   He must increase, but I must decrease.
   --John iii. 30.

   The heavens forbid But that our loves and comforts should increase, Even as our days do grow!
   --Shak.

2. To multiply by the production of young; to be fertile, fruitful, or prolific.

   Fishes are more numerous or increasing than beasts or birds, as appears by their numerous spawn.
   --Sir M. Hale.

3. (Astron.) To become more nearly full; to show more of the surface; to wax; as, the moon increases.

   Increasing function (Math.), a function whose value increases when that of the variable increases, and decreases when the latter is diminished; also called a monotonically increasing function.

   Syn: To enlarge; extend; multiply; expand; develop; heighten; amplify; raise; enhance; spread; aggravate; magnify; augment; advance.

   Usage: To Increase, Enlarge, Extend. Enlarge implies to make larger or broader in size. Extend marks the progress of enlargement so as to have wider boundaries. Increase denotes enlargement by growth and internal vitality, as in the case of plants. A kingdom is enlarged by the addition of new territories; the mind is enlarged by knowledge. A kingdom is extended when its boundaries are carried to a greater distance from the center. A man's riches, honors, knowledge, etc., are increased by accessions which are made from time to time.

n. (context mathematics English) Any function of a real variable whose value increases (or is constant) as the variable increases.