Features of Rational Functions
Rational Equations and LImits
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
Use the function 
to determine the graph’s behavior right of 3.
lim x->3^+=oo
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 do the initials WWW stand for?
A: World Wide Web
200
Determine the horizontal asymptote of the following function.
f(x)=1/x^2
y=0
200
Use the function f(x)=(3(x+3))/(x^2+x-12) to determine the graph’s behavior left of -4.
- Write your answer in limit notation.
lim x->4^- =-oo
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
Which two states are outside the continental US?
Alaska, Hawaii
300
Find the x and y value of the removable disconinuity.
f(x)=(x^2+2x-15)/(x^2+3x-10)
(-5, 8/7)
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
Who was the Greek god of the sea?
Poseidon
400
Identify the asymptotes of the following function.
f(x)=(3x^2-3)/(2x^2-8)
Vertical Asymptotes: x=2, x=-2
Horizontal Asymptote: y=3/2
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
Write all transformations of
g(x)=(-2)/(x+2)+2
of the function
f(x)=1/x
Transformations: Left 2, Up 2, Reflection, Stretch by 2
400
What is 15% of 300?
45
500
Find the slant asymptote of the following rational function.
f(x)=(2x^2+3x-15)/(x+1)
y=2x+1
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)=4+(7)/(x-1)
and describe the transformations from
f(x)=1/x
Transformations: Right 1, Up 4, Vertical Stretch by 7
500
Which Renaissance artist designed an early prototype of the helicopter?
Leonardo Da'Vinci