Name: ___________________________________________ Date: _____________________________ Period: ____________
Algebra 2 Section 8.2 Graphing Rational Functions Practice
Very Important Function Vocabulary
Term
Definition
Example
𝑦=
𝑥2
𝑥 2 +1
continuous
𝑦=
(𝑥+2)
(𝑋+2)(𝑥+3)
discontinuous
𝑦=
(𝑥+4)
(𝑥−4)
vertical asymptote
𝑦=
hole
(𝑥 2 −3𝑥−4)
(𝑥−4)
a) 𝑦 =
b) 𝑦 =
2𝑥
𝑥−3
𝑥−2
𝑥 2 −2𝑥−3
horizontal asymptote
c) 𝑦 =
𝑥2
2𝑥−5
Part 1: The Simple Rational Functions
Example 1) Graph the parent function of the Reciprocal Function Family y 
1
x
a) What is the domain?
b) What is the range?
c) As x approaches infinity, y approaches
d) As x approaches negative infinity, y
approaches
e) What are the asymptotes of the function?
𝟒
Example 2) Given: 𝒚 = 𝒙
a) Give the transformations from the parent function
b) Graph the function.
c) Identify the domain and range.
d) As x approaches infinity, y approaches
e) As x approaches negative infinity, y approaches
f) What are the asymptotes of the function?
𝟏
Example 3) Given: 𝒚 = 𝒙+𝟐 + 𝟒
a) Give the transformations from the parent function
b) Graph the function.
c) Identify the domain and range.
d) As x approaches infinity, y approaches
e) As x approaches negative infinity, y approaches
f) What are the asymptotes of the function?
Part 2: Getting More Complicated…. So here is a cheat sheet.
When Graphing Rational Functions – Don’t Forget YOU CAN USE YOUR CALCULATOR!
Fat
Factor (if possible)
Cats
Cancel (if possible)
Run Down
Removable Discontinuity
(find the “hole”)
1) Put what you canceled equal to zero. This is the x-coordinate of
your hole
2) Plug this x in to get the y-coordinate
Virginia
Vertical Asymptote
(put denominator equal to zero and solve)
Hills
Horizontal Asymptote
(Look at the degree of polynomials – *see below)
Grabbing
Graph
Delicate
Domain
(All real #s except what x )
Roses
Range
(1st -- asymptotes and holes, then find points in calc)
(All real #s except what y )
Horizontal Asymptote Trick: Look at the degrees of the numerator and denominator:
Same/same,
coefficients are
lame.
4𝑥 + 3
𝑦=
5𝑥 − 2
HA: 𝒚 =
𝟒
𝟓
Bigger below,
y=0
Big on top,
stop
3
𝑦=
𝑥−4
𝑥2 + 3
𝑦=
2𝑥 − 1
HA: 𝒚 = 𝟎
HA: N/A
Example 4:
f (x) =
Example 5:
1
x -1
y=
x
x -1
Domain:
Holes:
V.A.:
H.A.:
Range:
Domain:
Holes:
V.A.:
H.A.:
Range:
Domain:
Holes:
V.A.:
H.A.:
Range:
Domain:
Holes:
V.A.:
H.A.:
Range:
Example 6:
f (x) =
Domain:
Holes:
V.A.:
H.A.:
Range:
Example 7:
x(x +1)
(x +1)(x -1)
f (x) =
2x -1
x + 2x - 8
Domain:
Holes:
V.A.:
H.A.:
Range:
2