Continuity

Do Now: An volt battery to a 12 volt battery 7 seconds after being turned on. Graph the battery

voltage against electrical circuit switches instantaneously from a 6 time. Write the function

represented by the graph. What can you say about the continuity of this function?

When is a function continuous at a point?

A function f(x) is continuous at c if:

a. f(c) exists

b.

c.

limx c

exists

lim ( )x c

f c

Types of discontinuity:

1. Jump

2. Removable (hole)

3. Infinite (vertical asymptote)

4. Oscillating

How can we make a function continuous?

4

2)(

2

x

xxf

Redefine the function as piecewise(Fill in the hole)

2,2

2,2)(

xkx

xxxf

Set branches =, sub in x, and solve for coefficient or constant