Solution Manual for Precalculus, 6th Edition

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Solution Manual for Precalculus, 6th Edition offers a comprehensive guide to solving every question in your textbook, helping you master the material.

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INSTRUCTOR’S SOLUTIONS
MANUAL
DANIEL S. MILLER
Niagara County Community College
PRECALCULUS
SIXTH EDITION
Robert Blitzer
Miami Dade College

iii
TABLE OF CONTENTS
PRECALCULUS 6 E
Chapter P Prerequisites: Fundamental Concepts of Algebra 1....................................................1
Chapter 1 Functions and Graphs .............................................................................................127
Chapter 2 Polynomial and Rational Functions........................................................................259
Chapter 3 Exponential and Logarithmic Functions.................................................................411
Chapter 4 Trigonometric Functions ........................................................................................489
Chapter 5 Analytic Trigonometry ...........................................................................................657
Chapter 6 Additional Topics in Trigonometry ........................................................................771
Chapter 7 Systems of Equations and Inequalities ...................................................................919
Chapter 8 Matrices and Determinants ...................................................................................1057
Chapter 9 Conic Sections and Analytic Geometry................................................................1161
Chapter 10 Sequences, Induction, and Probability..................................................................1281
Chapter 11 Introduction to Calculus .......................................................................................1381

Chapter P
Prerequisites: Fundamental Concepts of Algebra
1
Section P.1
Check Point Exercises
1. 2 2
8 6( 3) 8 6(13 3)x+ − = + −
2
8 6(10)
8 6(100)
8 600
608
= +
= +
= +
=
2. a. Since 2014 is 14 years after 2000, substitute 14
for x.
2
2
4 330 3310
4(14) 330(14) 3310
8714
T x x= + +
= + +
=
The average cost of tuition and fees at public
U.S. colleges for the school year ending in
2014 was $8714.
b. The formula underestimates the actual answer
by $179.
3. The elements common to {3, 4, 5, 6, 7} and
{3, 7, 8, 9} are 3 and 7.
{3, 4,5, 6, 7} {3, 7,8,9} {3, 7}∩ =
4. The union is the set containing all the elements of
either set.
{3, 4,5, 6, 7} {3, 7,8,9} {3, 4,5, 6, 7,8,9}∪ =
5. 9, 1.3, 0, 0.3, , 9, 10
2
π 
− − 
 
a. Natural numbers: 9 because 9 3=
b. Whole numbers: 0, 9
c. Integers: 9, 0, 9−
d. Rational numbers: 9, 1.3, 0, 0.3, 9− −
e. Irrational numbers: , 10
2
π
f. Real numbers: 9, 1.3, 0, 0.3, , 9, 10
2
π
− −
6. a. 1 2−
Because 2 1.4,≈ the number inside the
absolute value bars is negative. The absolute
value of x when x < 0 is –x. Thus,
( )1 2 1 2 2 1− = − − = −
b. 3
π −
Because 3.14,
π ≈ the number inside the
absolute value bars is positive. The absolute
value of a positive number is the number itself.
Thus,
3 3.
π π− = −
c. x
x
Because 0, .x x x> =
Thus, 1
x x
x x
= =
7. 4 (5) 9 9− − = − =
The distance between –4 and 5 is 9.
8. 2 2
7(4 3 ) 2(5 )x x x x+ + +
2 2
2 2
2
7(4 3 ) 2(5 )
28 21 10 2
38 23
x x x x
x x x x
x x
= + + +
= + + +
= +
9. 6 4[7 ( 2)]x+ − −
6 4[7 2)]
6 4[9 ]
6 36 4
42 4
x
x
x
x
= + − +
= + −
= +

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