Continuity Function

A continuous function on is a function whose can be described by the motion of a particle traveling along it from a point to another without moving off its curves. A function is said to be continuous at a point if and only if it is continuous from left as well as from the right. To clarify the concept of continuity, we can simply say that if a function is continuous on an interval, the graph of the function will not have any jumps or holes on that interval.

A function f is defined on a closed interval [a,b] is said to be continuous at the end point a if it is continuous from right at a. Also a function is continuous at the end point b of [a,b]if it is continuous from left at b. A function f is said to be continuous at each and every point of the interval.

A Function f is said to be discontinuous at a point c of its domain if it is not continuous at c. The point c is then called a point of discontinuity of the function.

Every constant function is continuous. All closed form functions are continuous on their (whole) domain. A closed-form function is any function that can be obtained by combining constants, powers of x, exponential functions, radicals, logarithms, and trigonometric functions (and some other functions we shall not encounter in this text) into a single mathematical formula by means of the usual arithmetic operations and composition of functions.

Let f(x) be a function defined on an interval around a. We say that f(x) is continuous at a if

A function "f" in interval [a,b] is said to be a continuous function when the Graph drawn for f(x) is a smooth line or curve without any break in it. Such curve or line can be drawn by the continuous motion of a pencil in a sheet of paper. And Discontinuous function is just opposite of the continuous function , the function "f" is said to be discontinuous function when the graph drawn for f(x) is consists of disconnected curves or lines.