Features of Rational Functions
Solving Rational Equations
Trig in the Coordinate Plane
Ferris Wheel Problems
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
An angle theta is in quadrant 4.
Determine if sin and cos are positive or negative.
Cos is positive
Sin is negative
100
The following equation models the height (in meters), h, of a rider on a ferris wheel after t seconds. Find the height of the rider after 17 seconds. Round to the nearest hundreth.
h=28+22sin(9t)
37.99 meters
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
sin(theta)=5/13
in Quadrant 2.
Find
cos(theta)
cos(theta)=-12/13
200
The following equation models the height (in meters), h, of a rider on a ferris wheel after t seconds. Find the radius and center height of the ferris wheel.
h=28+22sin(9t)
radius: 22m
center: 28m
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
sin(theta)=-sqrt(5)/sqrt(30)
in Quadrant 4.
Find
cos(theta)
cos(theta)=5/sqrt(30)
300
The following equation models the height (in meters), h, of a rider on a ferris wheel after t seconds. How long does it take for the wheel to make one full rotation.
h=28+22sin(9t)
40 seconds
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
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
tan(theta)=-sqrt(11)/5
in Quadrant 2.
Find
sin(theta) and cos(theta)
sin(theta)=sqrt(11)/6
cos(theta)=-5/6
400
Jake is on a ferris wheel that has a radius of 32m. He starts in a cart at the bottom of the wheel which is 8m off the ground. It takes 90 seconds to complete one full rotation.
Write a function to model Jake's height after t seconds.
h(t)=-32cos(4t)+40
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
tan(theta)=3/4
in Quadrant 3.
Find
sin(theta) and cos(theta)
sin(theta)=-3/5
cos(theta)=-4/5
500
Frankie is on a ferris wheel that has a radius of 40m. He starts in a cart at the bottom of the wheel which is 5m off the ground. It takes 72 seconds to complete one full rotation.
Determine Frankie's height after 25 seconds. Round to the nearest hundreth.
67.94m
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