Features of Rational Functions
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.
List the possible extraneous solutions for the rational equation below. How do you know?
4/(x-5)-(2x)/(x+1)=1/((x-5)(x+1))
x=5 and x=-1 could be extraneous because when you plug them in, you get 0 in the denominator.
An angle theta is in quadrant 4.
Determine if sin and cos are positive or negative.
Cos is positive
Sin is negative
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
Is the following function even, odd or neither?
4sin(2x)-1
Neither
What day is Star Wars Day?
May 4th
Determine the domain and range of the following function.
f(x)=1/x^2
Domain: All real numbers except 0
Range: y>0
Solve for x. Determine if each solution is real or extraneous.
(4)/(x-7)=(2)/(x)
x=-7 , real
sin(theta)=5/13
in Quadrant 2.
Find
cos(theta)
cos(theta)=-12/13
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
Is the following function even, odd or neither?
-3cos(x)+2
Even
What is the name of the longest river in Africa?
The Nile River
Is the following functions even, odd or neither?
f(x)=1/x
Odd
Solve for x. Determine if each solution is real or extraneous.
2/(x-1)=3/(x+4)
x=11 , real
sin(theta)=-sqrt(5)/sqrt(30)
in Quadrant 4.
Find
cos(theta)
cos(theta)=5/sqrt(30)
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
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
Name two Taylor Swift albums.
Taylor Swift, Fearless, Speak Now, Red, 1989, Reputation, Lover, Folklore, Evermore, Midnights
Identify the asymptotes of the following function.
f(x)=1/x^2
Vertical Asymptote: x=0
Horizontal Asymptote: y=0
Solve for x. Determine if each solution is real or extraneous.
(-x)/(x-3)+(2x-1)/(x+1)=(-4)/((x-3)(x+1))
x=1 , real
x=7, real
The terminal ray of an angle passes through the point
(-5, sqrt11)
Find
sin(theta) and cos(theta)
sin(theta)=sqrt(11)/6
cos(theta)=-5/6
Jake is on a ferris wheel that has a radius of 32m. He starts in a cart at the far right of the wheel which is 40m 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)=32sin(4t)+40
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
In what song does Taylor sing: “Cause the players gonna play, play, play, play, play”?
Shake it Off
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.
Solve for x. Determine if each solution is real or extraneous.
x/(x-2)+(-3)/(x+2)=8/((x+2)(x-2))
x=-1, real
x=2, extraneous
The terminal ray of an angle passes through the point (-4, -3).
Find
sin(theta) and cos(theta)
sin(theta)=-3/5
cos(theta)=-4/5
Frankie is on a ferris wheel that has a radius of 40m. He starts in a cart at the far right of the wheel which is 45m off the ground. It takes 72 seconds to complete one full rotation.
Determine Frankie's height after 20 seconds. Round to the nearest hundreth.
84.39m
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
Which continental US state does not do Daylight Savings?
Arizona