Domain/Range and Factoring
Solving Rational Functions
Horizontal and Vertical Asymptotes
Transformations
100
What are the factors of
x^2-4x-5?
What is
(x-5)(x+1)
100
Solve:
(x-1)/(x+5)=2/5
What is
x=5
100
Find the horizontal asymptote of
y=(2x-5)/(x^2-4x-5)
What is
y=0
100
Given the function
f(x)=1/x
,describe the transformations that result in the function
g(x)=1/(x-3)
What is
Shift right 3 units
200
What are the factors of
x^2-2x-3?
What is
(x-3)(x+1)
200
Solve:
(x+3)/(x-6)=1/4
What is
x=-6
200
Find the horizontal asymptote of
y=(2x^2-5)/(x^2-4x-5)
What is
y=2
200
Given the function
f(x)=1/x
,describe the transformations that result in the function
g(x)=1/(x)+2
What is
Shift up 2 units
300
What is the domain and range for the following rational function?
What is
Domain:
(-oo,2) U (2,oo)
Range:
(-oo,0)U(0,oo)
300
Solve:
y/(y-2)+3=10/(y-2)
What is
y=4
300
Determine the excluded values of x for
y=(2x+1)/((3x)(5x-1))
What is
x=0 and x=1/5
300
Given the function
f(x)=1/x
,describe the transformations that result in the function
g(x)=-1/(x)
What is
Reflect over the x-axis
400
What is the domain and range for the following rational function?
What is
Domain:
(-oo,-1) U (-1,oo)
Range:
(-oo,4) U (4,oo)
400
Solve:
y/(y-1)+4=6/(y-1)
What is
y=2
400
Find the vertical asymptote(s) of
y=(2x^2-5)/(x^2-4x-5)
What is
x=-1 and x=5
400
Given the function
f(x)=1/x
,describe the transformations that result in the function
g(x)=-1/(x-3)-4
What is
Reflect across the x-axis
Shift right 3 units
Shift down 4 units
500
What is the domain and range of the function
y=(2x+1)/((x+3)(x-5))
What is
Domain:
(-oo,-3)U(-3,5)U(5,oo)
Range:
(-oo,0)U(0,oo)
500
If y varies inversely as x, and x=4 when y=6, find the constant of variation.
What is
a=24
500
What are the Vertical and Horizontal Asymptotes of
y=2/(x-3)+5?
What is
Vertical Asymptote:
x=3
Horizontal Asymptote:
y=5
500
Given the function
f(x)=1/x
,describe the transformations that result in the function
g(x)=-1/(x-1)+3
What is
Reflect over the x-axis
Shift right 1 unit
Shift up 3 units