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A function is continuous at a point x=c if the following three conditions are met...
Graph Examples
Notation
The function has to be defined when x=c, if there isn't a point for example, a hole then it is discontinuous.
Equation Examples
Jump- PW
Hole- Rational
Vertical Asymptote- Rational
PW fx-
...., x<5
...., x>5
If theres no equal sign on the inequalitites the fx is not defined
Rational fx-
The denominatore is 0. The numerator doesn't matter
function defined f(c) is defined..
f(a) is defined
Replace this text with a plain English explanation of what this condition means.
Notation
Graph Examples
Equation Examples
In this space, upload some hand-drawn pictures of graphs where the limit does not exist and where it does exist. Be sure to point out where that is happening. Also show some where the function is defined and some where the function is not defined. Delete this text when you're done.
Examples where the limit doesnt exist jump- piecewise f(x) asymptote- rational f(x)
PW f(x)- the 2 pieces dont equal each other at that point
Rational f(x)-
0/0- hole
#/0- vertical asymptote
limit exists, lim f(x)= lim f(c).
limf(x) exist
x--a
the limit at f(x) nd c must be equal at the same y value.
Notation
Graph Examples
Equation Examples
We're looking for a hole-> rational fx by 0/0 with a dot-> piecewise fx
underneath
f(c) =lim f(x)
x--c
lim f(x)= f(a)
x--a