Transcript Graphing Rational Functions with Notes

GRAPHING RATIONAL FUNCTIONS
GRAPHING RATIONAL FUNCTIONS
1.
2.
3.


Factor
Determine where discontinuities would occur in the
graph
Graph any asymptotes on the graph and pick points
on both sides to locate the branches of the function
If factors cancel, then you have a point of
discontinuity (hole)
If factors remain in the denominator, you have a
vertical asymptote(s)
HORIZONTAL ASYMPTOTES
1.
2.
3.
If the degree of the numerator is bigger than
the degree of the denominator, then there is
NO H.A. (top-heavy)
If the degree of numerator is smaller than the
degree of the denominator, then the HA is at
y=0 (bottom heavy)
If the degree of numerator is equal to degree
of the denominator, then the HA is equal to
the leading coefficients (equal weight)
PARENT FUNCTION
𝑓 𝑥 =
Domain:
Range:
VA:
HA:
Hole:
1
𝑥
𝑦=
1
𝑥+2
Domain:
Range:
VA:
HA:
Hole:
𝑦=
𝑥 2 +7𝑥+12
𝑥 2 +9𝑥+20
Domain:
Range:
VA:
HA:
Hole:
𝑦=
3𝑥 2 −13𝑥−10
𝑥−5
Domain:
Range:
VA:
HA:
Hole:
𝑦=
𝑥 2 +2𝑥−3
𝑥 2 +𝑥−2
Domain:
Range:
VA:
HA:
Hole:
𝑦=
𝑥
𝑥 2 −2𝑥−3
Domain:
Range:
VA:
HA:
Hole:
𝑦=
𝑥 2 −9
𝑥−3
Domain:
Range:
VA:
HA:
Hole:
𝑦=
𝑥 2 −9
𝑥 2 −1
Domain:
Range:
VA:
HA:
Hole: