2.6 DAY 3 Slant Asymp 2.6 Notes Day 3
Today you will learn about:
How to recognize and work with Slant Asymptotes
2.6 DAY 3 Slant Asymp Slant (aka OBLIQUE) Asymptotes
Consider a rational function whose denominator is
of DEGREE 1 or Greater.
If the degree of the numerator is EXACTLY ONE MORE than the degree of the denominator,
the graph of the function has a SLANT ASYMPTOTE
Which of these functions has a Slant Asymptote?
2.6 DAY 3 Slant Asymp Slant (aka OBLIQUE) Asymptotes
Consider a rational function whose denominator is
of DEGREE 1 or Greater.
If the degree of the numerator is EXACTLY ONE MORE than the degree of the denominator,
the graph of the function has a SLANT ASYMPTOTE
Which of these functions has a Slant Asymptote?
this is the only
function shown
that has a
slant asymptote
No Slant Asymp.
since DEN is not
degree 1 or higher
No Slant Asymp. DEN
is degree 1 or higher,
but NUM degree is
two degrees away
from DEN degree.
2.6 DAY 3 Slant Asymp 2.6 Slant (i.e. oblique) Asymptotes
To find the equation of the slant asymptote, find
x2­x . Find the slant asymptote 1. f(x) = x +1
is DEN degree is 1
or higher?
yes
write answer starting with "y="
is NUM is 1 degree
away from DEN?
yes
Take a look at the graph
Graph y1=
Now graph the slant asymptote as y2
Graph y 1=
y 2=
y
­2
x
=
2.6 DAY 3 Slant Asymp 2.6 Slant Asymptotes
To find the equation of the slant asymptote, find q(x)
a. State the Domain
b. Identify all intercepts
c. Identify any vertical, horizontal, and slant asymptotes
you can find the x­intercepts from the
NUM factors, but watch for holes. This
will change your x­intercept answers.
x2­x­2
2. f(x) = x ­1
leading terms
reduce to x, so
there is no HA
you can find the y­intercepts by reducing
the constants in the NUM and DEN.
[­5,5]x[­10,10]
2
3. g(x) = x ­9
x+5
leading terms
reduce to x, so
there is no HA
you can find the x­intercepts from the
NUM factors, but watch for holes. This
will change your x­intercept answers.
you can find the y­intercepts by reducing
the constants in the NUM and DEN.
Note:
a. b.x­int:
y­int:
[­20,20]x[­40,30]
c. VA
HA
SA
2.6 DAY 3 Slant Asymp 1
4. h(x) = x­3
a.
b.x­int:
y­int:
c. VA
HA
SA
calc
value
at x=0
[­5,7]x[­7,7]
5. g(x) =
5x+20
x2+x­12
a.
b.x­int:
y­int:
calc
value
at x=0
[­10,10]x[­10,10]
c. VA
HA
SA
­5
or (0, ) 3
3
2.6 DAY 3 Slant Asymp 3
x
6. f(x)= 2
x ­4
a.
b.x­int:
y­int:
c. VA
HA
SA
[­7,7]x[­10,10]
2.6 DAY 3 Slant Asymp 2.6 Homework:
p 194: 51­68 ALL WPF Directions: Find Domain, VA, HA, SA
Skip Graphing the picture Skip finding x and y intercepts