1'6 Continuity

1
1.6 Continuity
2
A function is continuous at x c means that
there is no interruption in the graph of f at c.
The graph of f is unbroken at c, and there are no
holes, jumps, or gaps.
3
Definition of Continuity
4
You can say that a function is continuous on an
interval if its graph on the interval can be
traced using a pencil and paper without lifting
the pencil from the paper.
5
Continuity of Polynomial and Rational Functions

• 1. A polynomial function is continuous at every
  real number.
• 2. A rational function is continuous at every
  number in its domain.

6
Rational Functions need not be continuous on the
entire real line.
7
If a function is continuous at every number in an
open interval except c, then c is a discontinuity
of the function.
8
c is a removable discontinuity of f if the
graph of f has a hole at the point (c,L) where L
is the limit of f(x) as x approaches c.
9
c is nonremovable discontinuity if the
function cannot be made continuous at x c by
defining or redefining the function at x c.
10
Definition of Continuity on a Closed Interval
11
(No Transcript)
12
The Greatest Integer Function
13
http//www.mathematicshelpcentral.com/lecture_note
s/calculus_1_folder/continuity.htm
14
http//www.howardcc.edu/math/MA145/1.6/1.6.htm