Ch 7: Continuity, Discontinuity, IVT

what does it mean if a function is continuous

it is defined on an open interval including “a”

if you have to pick up your pen, the graph (is/isnt) continous.

isnt

Name the 3 types of discontinuities

1. hole (removable discontinuity)

2. infinite discontinuity

3. jump

what is a hole?

a point in graph where function isnt defined

what is an infinite discontinuity

if there are VA/HAs

what is a jump discontinuity

when limit DNE at a point

If a discontinuity can be fixed by adding an additional point, it is a ____ discontinuity. If it cannot be fixed by adding an additional point, it is a ____ discontinuity.

removable ; nonremovable

Name the 7 types of continuous functions

1. polynomials

2. rational

3. root

4. trig

5. inverse trig

6. exponential

7. log

If two functions f and g are continuous, then the sum, difference, product, and quotients of the two functions are also _____.

continous

for f(g(x)) only __ contributes to overall domain.

g(x)

for g(f(x)) only __ contributes to overall domain.

f(x)

Intermediate Value Thereom:
Suppose f is continuous on [a, b] and N is any num-
ber between f (a) and f (b), then there exists an x=c in just that f (c) = __.


N