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Chapter 5 –Rational Inequalities Quiz
KNOWLEDGE:
Name __________________
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1. a) Sketch the graph of f ( x)  5  2 x and its reciprocal on the same set of axes.
b) For the reciprocal function, determine the domain, range, intercepts,
positive/negative intervals and intervals of increase/decrease.
[8]
2. Determine the equation of the asymptotes for the following rational function.
f ( x) 
x2  1
x2
[3]
3. Solve algebraically
4
 2  3x
2x  3
[4]
4. Solve. Express your solution in interval notation.
1
0
x2
[3]
APPLICATION:
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5. Harold mows a lawn in 4 hours. Molly mows the same lawn in 5 hours. How long
would it take both of them working together to mow the lawn?
[3]
6. Sketch each of the following rational functions. Use any key points.
3x  4
4 x  16
a) f ( x) 
b) f ( x) 
x4
x4
[6]
MHF 4U
Chapter 5 Application Questions
1. Determine the intervals in which the reciprocal function of f(x)
increasing.
x + 1 is
2. It takes Frank 2 hours longer than Jane to carve a pumpkin for Halloween.
Together they can carve it in 1
hours. How long would it take for Frank to do
the job alone?
3. The harmonic mean of two numbers, a and b, is a number m such that the
reciprocal of m is the average of the reciprocals of a and b. Which of the
following is a formula for the harmonic mean of a and b?
a) m 
2ab
ab
b) m 
ab
2ab
4. This is the graph of
and
c) m 
ab
2
d) m 
2
ab
For what interval is
?
y
7
6
5
4
3
2
1
–7 –6 –5 –4 –3 –2 –1
–1
1
2
3
4
5
6
7
x
–2
–3
–4
–5
–6
–7
5. Members of a high school choir want to attend a national contest. After a signup, the choir director stated that the trip will cost $400 per choir member plus a
$1500 fee for the choir to participate.
a) Write an equation to represent the total average cost of the trip per choir member.
b) What is the horizontal asymptote of the function? What does it mean in
relationship to this problem? What is the vertical asymptote? What does it
mean in relationship to the problem.
c) Find the total average cost of the trip if 45 members attended.
d) How many members must attend to bring the total average cost to $425 per
member.
e) Graph the function.