
Rational Functions
Presentation
•
Mathematics
•
12th Grade
•
Medium
+3
Standards-aligned
Juan Montano
Used 12+ times
FREE Resource
10 Slides • 33 Questions
1
Rational Functions
2
Rational Functions are a division among two polynomials
They have asymptotes:
vertical
horizontal
oblique*
Characteristics
3
Vertical Asymptotes
4
Horizontal Asymptotes
5
If the degree of P(x) and Q(x) are equal
If the degree of P(x) is less than Q(x)
If the degree of P(x) is greater than Q(x)
6
Empty Points
7
Multiple Choice
y = 2
x = 1
x = 2
y = -1
8
Multiple Choice
Which asymptote(s) are determined by looking just at the denominator?
vertical
horizontal
end behavior
none
9
Multiple Choice
What are the equation of the asymptotes?
x=-3, y=1
x=3, y =1
x=-3, y =-1
x=3 y=-1
10
Multiple Choice
What are equations of the asymptotes?
x=-1 y = -3
x=1 y = -3
x=-1 y =3
x=1, y=3
11
Multiple Choice
What is the Vertical Asymptote?
y=x−6x−3
12
Multiple Choice
Select the option with the right equations of the asymptotes
13
Multiple Choice
How many vertical asymptotes does the function have?
None
1
2
3
14
Multiple Choice
Which of the following represents the vertical asymptote(s) for the function below?
f(x)=x2(x−4)(x+2)5
x=0,−4,2
x=4,−2
x=0,4, −2
x=−4,2
15
Multiple Choice
Which of the following represents the graph of f(x)=x2−161 ?
16
Math Response
17
Math Response
18
Multiple Choice
None
y=-2
y=2
y=0
19
Math Response
20
Multiple Choice
The horizontal asymptote equals zero when:
the degree of the numerator and denominator are equal
the degree of the numerator is less than the degree of the denominator
the degree of the numerator is greater than the degree of the denominator
the numerator equals zero
21
Multiple Choice
vertical
horizontal
slant
none
22
Math Response
23
Multiple Choice
What's the vertical asymptote of the function?
x = 5
x = 0
x =5 , x = -5
x = 25
24
Domain
25
Range
26
Domain and Range with hole(s)
27
Multiple Select
In finding the domain of the rational function
r(x)=q(x)p(x) where p(x) and q(x) are polynomial functions, all real numbers are allowed for x except . . .
(Check all that applies.)
The ones that would make the numerator zero. p(x)=0
The ones that would make the denominator zero. q(x)=0
The ones that would make the function zero. r(x)=0
The ones that would make the function undefined.
28
Multiple Choice
What is the domain of
y=x1 ?
x=−1
x=0
x=1
x=y
29
Multiple Choice
What is the range of
y=x1 ?
y=−1
y=0
y=1
y=x
30
Multiple Choice
Find the domain of
y=x+12 .
x=−1
x=0
x=1
x=2
31
Multiple Choice
Find the range of
y=x+12
y=−1
y=0
y=1
y=2
32
Multiple Choice
The domain of
y=x+2x−1 is
x=−2
x=−1
x=1
x=2
33
Multiple Choice
The range of
y=x+2x−1 is
y=−2
y=−1
y=1
y=2
34
Multiple Select
What is the domain of
y=(x+2)(x−3)(x−1)(x+4) ?
(Check all that applies.)
x=−2
x=−1
x=3
x=4
35
Multiple Choice
What is the domain of the rational graph?
Domain:
(-∞,1)U(1,∞)
All real numbers.
Domain:
(-∞,3)U(3,∞)
36
Multiple Choice
What is the Domain of the graph?
Domain: (-∞,-3)U(-3,∞)
All real numbers
Domain: (-∞,1)U(1,∞)
37
Multiple Choice
What is the Range of the graph?
{x∣x∈ℜ , x=−3 ∣}
All real numbers
{y∣y∈ ℜ , y=4∣}
38
Multiple Choice
Find the domain for the function f(x)=3x+62x−1
x cannot equal to 2
x cannot equal to -2
x cannot equal to 3
All real numbers
39
Multiple Choice
Find the range for the function f(x)=3x+62x−1
x cannot equal to -2
y cannot equal to 2/3
y cannot equal to -2/3
All real numbers
40
Multiple Choice
Find the domain of the function. f(x)=2x+4x
x cannot equal to 2
x cannot equal to 4
x cannot equal to -2
All real numbers
41
Multiple Choice
Find the range of the function. f(x)=2x+4x
x cannot equal to 1/2
y cannot equal to 1/2
x cannot equal to -2
All real numbers
42
Multiple Choice
Find the domain of the function f(x)=x+8x3
x cannot equal to 2
x cannot equal to -2
x cannot equal to -8
All real numbers
43
1) Graph all the asymptotes (vertical and horizontal)
2) Plot any empty point (hole) in the plane
3) Evaluate your function for two values at each side of each vertical asymptote
Graphing
Rational Functions
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