continuous function
nounUK /kənˈtɪnjuəs ˈfʌŋkʃən/
US /kənˈtɪnjuəs ˈfʌŋkʃən/
A continuous function is a math rule that draws a smooth line you can trace without lifting your pencil.
The teacher showed that a straight line is a continuous function because it has no breaks.
OTHER MEANINGS
2. In topology, a function where the preimage of every open set is open.
Topologists define a continuous function using open sets rather than pencil strokes.
3. A function with no jumps, holes, or breaks at any point in its domain.
The function f(x) = x² is continuous everywhere on the real line.
4. A mapping that preserves closeness, so nearby inputs give nearby outputs.
Because the map is a continuous function, points that start close stay close after mapping.