1. Continuity
Lesson 3.2

4. In this context, what do you think continuity means?
Continuity in Context !!??
In this context, what do you think continuity means?

5. Intuitive Look at Continuity
A function without breaks or jumps
The graph can be drawn without lifting the pencil 

6. Strange Functions A jump in the graph But it is a function
The limit at 3 does not equal the value of the function at 3
The function does not exist at x = 0

7. Definition of Continuity at x = c
Three conditions required
f(c) is defined
exists
Which condition is violated by each of our strange functions?

8. Continuity on Closed Interval
Given closed interval [a, b] …
f(x) continuous if
Continuous on the open interval (a, b)
Continuous from right at x = a
Continuous from left at x = b
Example

9. Where Are They Continuous?
Polynomial Functions
Rational Functions
Root Functions
Exponential Functions
Logarithmic Functions

10. Where Are They Continuous?
Try it out … where are these functions continuous?
Where are they discontinuous

11. Assignment
Lesson 3.2
Page 175
Exercises 1 – 27 odd