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

The function is continuous at − {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 is continuous at , because its constituent functions are polynomial and the side limits at the points of division coincide.

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.