AP Calculus AB Unit 1.2 Day 2 Notes: Limits at Infinity & End Behavior Models (LEBM, REBM, EBM) | Latest Updated 2026–2027 | AP Exam Review

1.2 Day 2 Notes LEBM, REBM, EBM
SWBAT use end behavior models to solve for limits at infinity

Warm Up

For 1-3, given f ( x) , identify the following information using limits with proper documentation.

a) Any vertical asymptotes. You must create a table for each vertical asymptote, which shows
appropriate left and right hand tables values, then summarize with one sided limit notation, stating
the appropriate infinities from the analysis of your table values.
÷ -




b) Any horizontal asymptotes. You must identify the applicable end behavior models, then apply
lim and lim with the end behavior models. Remember, DNE is never acceptable answer on its
x x

own! You must go deeper and use end behavior rules to note the applicable infinity for any DNE


:¥s¥i¥¥§≠◦
cases.
¥n÷fk)=
is
-




1. EBM


¥n +flx)= (
,gfk)=¥sÉ→=¥%¥×≠o
I


µ;ggµ=• (
3×+51--0


µ,ygµ , , ≠




limfk-I.ms#s--I7abx-VAatx-.o.-gfi;gfkD---A #-)
✗→
-
D




Aaty=o
%fl×)=0
2. =

-4¥g) =
-4-12×-84
✗ +7
=

-12%-8,1
EBM
-12¥
:




¥88k)=¥%_¥×=¥: -12 ftp.fl-D-II?-E-x-- ¥?-12

I ×ffl×)= -12
,ffl×)=
-12
HA aty -12
-




✗ +71=0 1%11×1=0 E)
✗ ≠ -7



VA at ✗= -7
9+fk)=
- A
(E)

, EBM : 2¥

3. =2!=2tK
sfl×)=¥%2¥=y2× 7•fk)=¥%2¥=y2×
yflD=• ¥7.1k)= -
•
NOMA

× -1+-0
VAatx-lfiry.LK) =-D E)
✗ 1=1



7+81×1=-0 (




ax b
4. If the graph of y has a horizontal asymptote at y 2 , a vertical asymptote at x 4 and an
x c
x-intercept of 1.5, then a b c ?

Recall that when working with rational functions you determine the x-intercept by setting the numerator
= 0.


a¥= -2 a= -2
¥¥ˢ=O _2
✗+ c- 0
-2×+6=01×-4)
4tC=0
-




2x = -
b
C. =
-4

b- 2×-245--3


-2-3-4

= -9