Continuous Function

Polynomial, rational, radical, exponential, logarithmic and trigonometric functions are continuous at all points of their domain.

Continuous Function

The function Function is continuous at Any Real Number − {3}. At x = 3 it is not continuous because the function does not exist at this point.

Piecewise Functions

Piecewise functions are continuous if every function is in its interval of definition,and if the functions match their side limits at the points of separation of their intervals.

The function Piecewise Function is continuous at Any Real Number, because its constituent functions are polynomial and the side limits at the points of division coincide.

Piecewise Function

Operations with Continuous Functions

If f and g are continuous at x = a, then:

f + g is continuous at x = a.

f · g is continuous at x = a.

f/g is continuous at x = a, if g(a) ≠ 0.

f ο g is continuous at x = a.