TIC-TAC-TOE
Rational Functions
Evaluation
Knowledge/Comprehension
Analysis
Graph each of the following rational
functions:
Matching:
Suppose that the average time (in hours)
h(t), that a new production team takes to
assemble one unit of a product is given by:
x2
f  x 
x 1
x6
h  x 
x 1
x4
g  x 
x 1
x8
k  x 
x 1
a. What similarities do you see?
b. What differences do you see? Explain
i)
ii)
iii)
 x  3 x  1
 x  2  x  5
 x  3 x  2 
f  x 
 x  2  x  5
 x  3 x  1
f  x 
 x  2  x  5
f  x 
h t  
3t  5
2t  1
h(t )  0 , t  0
Where t is the number of days of training
for the team.
A. What is the horizontal asymptote
B. What does this mean?
See attached sheet for graphs a - c
Analysis
Application
Synthesis
Which of the following rational functions
will NOT have a graph with a vertical
asymptote?
Which of the following rational functions
has all of the following characteristic?
A. Crosses the x-axis at 3
B. Crosses the y-axis at 3
C. One vertical asymptote at x = 1
D. Domain of  , 2   2,1  1,  
Decide whether each statement is Always
true, Sometimes true, or Never true:
i)
ii)
iii)
iv)
v)
x3
x2  4
3
f  x  2
x  4x
3x 2  6
f  x  2
x 6
x4
f  x  2
x  4 x  12
x3
f  x 
x 1
f  x 
Application
Use the given rational function to answer
questions a – e: Provide written algebraic
work to support your answers
f  x 
A.
B.
C.
D.
E.
2 x 2  7 x  15
x2  9
Find the domain
In any exist, find the x-interecept(s)
In any exist, find the y-interecept(s)
In any exist, find the vertical
asymptote(s)
In any exist, find the horizontal
asymptote(s)
 x  3 x  2 
 x  2  x  1
 x  3
vii) g  x  
 x  1
 x  3
m  x 
viii)
 x  1
 x  3 x  2 
ix) p  x  
 x  2  x  1
 x  3 x  2 
r  x 
 x  2  x  1
vi) f  x  
Synthesis
Create one rational function that
meets all of the following criteria.
You may leave your answer in
factored form:
A.
B.
C.
D.
Only one vertical asymptote at x = 4
An x-intercept at x = -2
An oblique asymptote
Domain of  ,0   0, 4   4,  
f  x 
p  x
q  x
Where p(x) and q(x) are non-zero
polynomial functions.
A. The graph of f(x) will have a horizontal
asymptote when degree of p(x) is less
than the degree of q(x)
B. The graph of f(x) will have xintercepts where p(x) = 0
C. The graph of f(x) will have at least one
vertical asmptote
Knowledge/Comprehension
Use the “Graph C” on the attached sheet
for a – f:
A. As x approaches -4 from the left side,
the y-value approaches ____
B. As x approaches -4 from the right
side, the y-value approaches ____
C. As x approaches 2 from the left side,
the y-value approaches ____
D. As x approaches 2 from the right side,
the y-value approaches ____
E. As x approaches ∞, the y-value
approaches ____
F. As x approaches -∞, the y-value
approaches ____
8
6
4
Graph A
2
10
5
5
10
2
4
6
8
10
8
6
4
2
Graph B
10
5
5
10
2
4
6
8
8
6
4
Graph C
2
10
5
5
2
4
6
8
10
TIC-TAC-TOE
Think Outside the Box
Draw one straight segment to
make a perfect square
Move 3 of the sticks, and the eye,
to make the fish face the opposite
direction
There are two “A” pills and two
“B” pills and you must take exactly
one of each. How can you do this
if there is no way to tell the
difference between the pills?
Figure out what the following
Rebus puzzle says
You have 9 ball bearings. 1 of
them is slightly heavier than the
rest. You have an old time scale
and can make only 2 weighs.
How would you weigh the ball
bearings to determine the heavier
one? (you cannot tell the
difference from holding them)
Without moving the football,
move 2 of the posts to make the
same size and shaped goal
WITHOUT the ball between the
uprights.
How can you cut a cake into 8
equally sized pieces with ONLY 3
straight cuts and WITHOUT
moving any of the pieces?
Which way is the bus traveling,
left or right?
TAILR
RIALT
AIRTL
TLRIA
You have 10 candles. How can
you arrange them on a cake in
order to have exactly 5 rows, each
row containing exactly 4 candles?
(without breaking any of the
candles)