Name : ________________________
MHF4U1
Unit 3: Rational Functions
K/U
APP
/17
COM
/7
TH
/10
/17
KNOWLEDGE/UNDERSTANDING
1. Find the horizontal/slant asymptotes for the following rational functions:
[3K]
(a) f(x)
(b) f(x)
(c) y 
x2  9
x
2. Identify any holes in the graph of f(x)
. Graph the function.
1
[3K]
3. Solve the following equality. Show a geometric representation of your solution. [3K]
(a)
4. Solve the following inequality. Show a geometric representation of your solution.
(a)
[4K]
2
5. Graph the function:
[4K]
APPLICATION
1. Salt water flows into a large tank of pure water. The concentration of the salt in the tank at
t minutes is given by
, were c is measured in grams/liter. Properly label the
axes.
a. When does the concentration in the tank reach 5 grams/liter?
b. When is the concentration of salt in the large tank less than 3 grams/litre?
[7T]
3
COMMUNICATION
1.
Which graph represents
? Explain your reasoning.
A
B
C
D
Reasons:
4
[2C]
2. What is the geometric meaning of the equality 4/(X-2) = 3 ? Sketch the graph to show where
the solution would be.
[2C]
3. What is the geometric meaning of the rational inequality 1/(x+1)(x-2) < 0 ? Sketch the graph
and show where the solution(s) would be.
[2C]
4. Explain why the inequality
5. If
is a polynomial function, does
has no solution
[2C]
always have to have a horizontal asymptote? If no,
provide a counterexample.
[2C]
5
THINKING
1. Write an equation for the following scenarios:
[4T]
(a) A rational quadratic function with no Vas
(b) A rational quadratic function with one VA
(c) A rational quadratic function with two VAs
(d) A rational quadratic function with a slant asymptote
2. Determine a possible equation for each function:
A.
[4T]
B.
6
3. Write an equation for a rational function whose graph of the form f ( x) 
indicated features.

X-intercept of

Y-intercept of

VA with equation

HA with equation
4. Analyze and sketch the rational function:
[5T]
7
ax  b
has all the
cx  d
[4T]
BONUS +2
Determine the equation of a rational function with vertical asymptote
at
and a horizontal asymptote
8
, a hole