Math 121

Section 1.6

Continuity

Definition: Let C be a number in the interval (a,b), and let f be a function whose domain contains the interval (a,b). The function f is continuous at point C if the following condition is true.

1)

2)

3)

A function f is continuous on an interval (a,b), if f is continuous at every point on the interval (a,b)

Examples

1) Give the intervals where the function is continuous

f is continuous on

The graph of a continuous function is piecewise smooth.

2) Give the intervals where the function is continuous

f is continuous on

4) Give the intervals where the function is continuous

f is continuous on

5) Give the intervals where the function is continuous

f is continuous on

Three types of situations that make a graph discontinuous

1) A hole

2) A break in the graph or gap in the graph

3) A asymptote

Continuity of Rational and Irrational Functions

1) A polynomial function is continuous everywhere

2) A rational function is continuous on its domain

Examples

1) Give the intervals where the function is continuous

2) Give the intervals where the function is continuous

3) Give the intervals where the function is continuous

4) Give the intervals where the function is continuous

5) Give the intervals where f is continuous

6) Give the intervals where the function is continuous