Features of Rational Functions
Solving Rational Equations
Transformations of Functions
Random Trivia
100
What features occur at x = 1 and x = -2 for the following equation.
f(x)=(x-1)/((x-1)(x+2))
At x=-2, there is a vertical asymptote.
At x=1, there is a hole.
100
List the possible extraneous solutions for the rational equation below. How do you know?
4/(x-5)-(2x)/(x+1)=1/(x^2-4x-5)
x=5 and x=-1 could be extraneous because when you plug them in, you get 0 in the denominator.
100
Describe each transformation from f(x) in words. (example: right 2, down 4,...)
1. f(x+3)
2. 3f(x)
3. f(x-3)
4. f(x)-3
1. left 3
2. vertical stretch by 3
3. right 3
4. down 3
100
What day is Star Wars Day?
May 4th
200
Determine the domain and range of the following function.
f(x)=1/x^2
Domain: All real numbers except 0
Range: y>0
200
Solve for x. Determine if each solution is real or extraneous.
(5)/(x+1)+(3)/x=(-1)/(x+1)
x=-1/3 , real
200
f(x)=1/x
The graph below is a transformation of the function f(x). Use your knowledge of transformations to write an equation for the graph below.
1/(x+2)-3
200
What is the name of the longest river in Africa?
The Nile River
300
Is the following functions even, odd or neither?
f(x)=1/x
Odd
300
5/(x-1)+x/(x+1)=(-5)/(x+1)
x=0, real
x=-9, real
300
f(x)=1/x
The graph below is a transformation of the function f(x). Use your knowledge of transformations to write an equation for the graph below.
1/(x-1)-4
300
Name two Taylor Swift albums.
Taylor Swift, Fearless, Speak Now, Red, 1989, Reputation, Lover, Folklore, Evermore, Midnights, The Tortured Poets Department, The Life of a Showgirl
400
Identify the asymptotes of the following function.
f(x)=1/x^2
Vertical Asymptote: x=0
Horizontal Asymptote: y=0
400
Solve for x. Determine if each solution is real or extraneous.
(-x)/(x-3)+(2x-1)/(x+1)=(-4)/(x^2-2x-3)
x=1 , real
x=7, real
400
g(x)=(2x+3)/(x+2)
g(x) is a transformation of the function f(x).
Rewrite g(x) in the form
q(x)+(r(x))/(d(x))
and describe the transformations from f(x).
g(x)=2+(-1)/(x+2)
Transformations: Left 2, Up 2, Reflection
400
In what song does Taylor sing: “Cause the players gonna play, play, play, play, play”?
Shake it Off
500
f(x)=1/x and g(x)=1/x^2
Which of the following is not the same for f(x) and g(x)?
Domain, Range, Vertical Asymptote, Horizontal Asymptote
Range
f(x) range is all real numbers except 0.
g(x) range is y>0.
500
Solve for x. Determine if each solution is real or extraneous.
x/(x-2)+(-3)/(x+2)=8/(x^2-4)
x=-1, real
x=2, extraneous
500
g(x)=(4x+3)/(x-1)
g(x) is a transformation of the function f(x).
Rewrite g(x) in the form
q(x)+(r(x))/(d(x))
and describe the transformations from f(x).
g(x)=4+(7)/(x-1)
Transformations: Right 1, Up 4, Vertical Stretch by 7
500
Which continental US state does not do Daylight Savings?
Arizona