Get Math Help

GET TUTORING NEAR ME!

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Continuous Function

    Basic definition

    A continuous function is function with no jumps, gaps, or undefined points.

    Detailed definition

    There are several commonly used methods of defining the slippery, but extremely important, concept of a continuous function (which, depending on context, may also be called a continuous map). The space of continuous functions is denoted C^0, and corresponds to the k = 0 case of a C^k function.
A continuous function can be formally defined as a function f:X->Y where the pre-image of every open set in Y is open in X. More concretely, a function f(x) in a single variable x is said to be continuous at point x_0 if 
1.f(x_0) is defined, so that x_0 is in the domain of f. 
2.lim_(x->x_0) f(x) exists for x in the domain of f.

    Educational grade level

    college level (AP calculus AB)

    Find the right fit or it’s free.

    We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.