1. Continuity
Section 2.3

2. Continuity Application of limits
A function f is continuous at x = a if
f(x) exists
The limit of f(x) exists

3. Continuity at a Point
Continuous functions have graphs that can be sketched in one continuous motion without lifting your pencil.
The outputs vary continuously with the inputs and don’t jump from one value to another without taking on the values in between.

4. See p. 74

5. Interior Point:
A function f is called continuous at x = c if c is in its domain and

6. Endpoint:
A function y= f(x) is continuous at a left endpoint a or is continuous at a right endpoint b of its domain if

7. If a function is not continuous at a point c, then f is discontinuous at c, and c is a point of discontinuity of f. (c doesn’t have to be in the domain of f)

9. Types of Discontinuities
Removable
Jump
Infinite
Oscillating
See p. 76

10. Page 77 Exploration 1

11. Continuous Functions
A function is continuous on an interval if and only if it’s continuous at every point on the interval.
A continuous function is one that’s continuous at every point of its domain. (It doesn’t have to be continuous on every interval.)
Page 78 Properties of Continuous Functions
Composites of continuous functions are continuous.

12. Intermediate Value Theorem for Continuous Functions
A function y = f(x) that is continuous on a closed interval [a, b] takes on every value between f(a) and f(b). In other words, if d is between f(a) and f(b), then d = f(c) for some c in [a, b] .

14. pages 80-81 (2-30 even, 44) ======================== pages 80-81 (3-9 odd, 19-29 odd)