Discontinuities
One-sided Limits
Two-sided Limits
Domain & Range
Miscellaneous
100
What are the 3 types of discontinuity?
-Jump
-Infinite
-Point/ removable
100
lim f(x)
x--> -1 -
1
100
A limit overall exists if...
The limits from the left and right side are equal.
100
What's the domain? Specify open or closed brackets.
(-infinity, +infinity)
100
f(3)=
1
200
what is the meaning of a discontinuous function?
A Discontinuous function is a function that includes breaks, holes, or gaps.
200
lim f(x)
x--> 1+
3
200
lim f(x)
x--> 3
2
200
What's the domain? (Specify closed or open brackets)
(-3, 1]
200
f(3)=
undefined
300
x--> 1-
neg. infinity
300
lim f(x)
x--> 1
DNE
300
What's the range? Specify closed or open brackets.
[-5, 4]
300
State the end behavior using limits.
lim f(x) = -infinity
x--> -inf
lim f(x)= infinity
x--> +inf
400
At which x-values, is the graph discontinuous?
x=-4, 2, 4
400
lim f(x)
x--> 0-
0
400
lim f(x)
x--> 2
infinity
400
What's the range? Specify open or closed brackets.
(-infinity, -1) U (2, infinity)
400
For what values of x is f(x)= 2 ... Estimate
x=-3.8, -1.3, 3.1
500
State the type(s) of discontinuity along with the location of each.
-Infinite at x=0
-Point at x=2
-Jump at x=4
-Point at x=6 (also jump)
500
lim f(x)
x--> 4+
4
500
lim f(x)
x--> 3
DNE
500
What's the domain? Specify closed or open brackets.
(-infinity, -1) U (-1, 4) U (4, infinity)
500
State the increasing intervals of the graph.
(-infinity, -5) U (4, infinity)