Precalculus: A Self-Teaching Guide (Wiley Self-Teaching Guides)

220 Pages·2001·2.22 MB·English

by  Steve Slavin Ginny Crisonino

Precalculus
A Self-Teaching Guide

Steve Slavin
Ginny Crisonino

®

John Wiley & Sons, Inc.
[New York « Chichester * Weinheim + Brisbane + Singapore + Toronto
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Contents

11 The Basics
Pretest, 2
Exponens, 5
Polynomials, 10
Rational Exponent and Radicals, 16
Factoring, 17
Basic Geomerr, 24
Appliation, 28

2 Functions
1 Definition of Function, 33
2 Operations on Fancions, 41
3 Composite Functions, 43
44 vere Functions, 45

3 Graphs of Functions
1 Ioerepts, $3
2 Slope ofa Staight Line, 57
13 Webing she Equation of a Stzight Line, 59
4 Guaphs of Linear Functions, 62
5 Graphs of Quadratic Functions, 67
{6 Graphs of Polyonial Functions of Degree 3 and Higher,

%6

33

32
CONTENTS

7 Asymptots, #2
1 Oblique Arymptotes and Graphs of Rational Functions, 68

Exponential and Logarithmic Functions
1 Exponential Functions, 103,

2 Logarithmic Functions, 108

3 Properties of Logasithie Functions, 111

“4 Solving Logarithmic Equations, 114

5 Applications, 119

‘Teigonomery
‘Angles and Thee Measure, 127

Righ-Tiangle Tigonomecy, 132
‘TeigonomerricFuncons of Any Angle, 134
Graphs ofthe Basic TigonometrieFuesons, 140
Inverse Teigonometrc Functions, 142
Aplications, 146

Analytic Trigonometry

1 Using Fundamental denies, 152

2 Verihing Tgonomeeic Lente, 156

2 Solving Tigonometic Equations, 159

4 Sum and Dierence Formals, 164

5. Maltple Angle and Produc-1o-Sum Formulas, 169

Additional Topics in Trigonometry
1 LawofSines, 178

2 Lawof Coins, 187

3. Areaof Triangle, 191

Miscellaneous Topics
1 Solving Systems of lnequaies and Liner Programming, 196
2 Paral Fraction Decomposition, 204

Index

103

27

152

178

196

2
The Basics

Before proceeding to precalculus, we'll review some basic concepts.
This chapter provides a bridge from elementary algebra to intermediate
algebra and other topics in precalculus. Most of these concepts should
bbe somewhat familiar, and you should be able ro quickly pick up where
you left off in algebra, whether it was last week, last year, or even the
last millennium,

‘When you've completed this chapter you should be able to work
swith:

‘+ exponents
+ polynomials

‘+ rational exponents and radicals
+ factoring

+ basic geometry

* applications

Before we begin, try the following pretest to get an idea of how
:much review you need, if any. If you get a perfect score on the pretest,
‘you can skip chapter 1 and go directly to chapter 2. To learn precaleu
Tus you have to have your intermediate algebra down cold.
2__PRECALCULUS

PRETEST

Simplify the following expressions. Do not leave negative exponents in
Your final answer Leave all answers in fully reduced form,

Part 1: Exponents
Simplify the following:

yy 20% 3. Go? an
5.42 «( 22+ 8 (24
3 ee 10. (:

art 2: Polynomials

1 2437-404 5y 12 (50-387

13, 7a'4a?~ 5a) 2a%a?~ 62°) 14 wy

15. 70°ta?~ 5a) 20°GaV-607) 16. @0+8)"-(20-y
17. (Ue + Au? —5u)~ (aur? ~ 30 +5)

18, (907 + 125987+ 1508) +36

19. (y)- 187-6 + ty) + (ay 2647)

Part 3: Factoring

Factor the following:

20. 152-364 12 21. 10672 sb 22.2 484416
2-718 24, 30'~5ab— 126425. = 100
26. 4x¢—16 27. 8-27 myst

29, 2ax-s bx + 2ay + by

Part 4: Rational Exponents and Radicals
‘Simplify the following:

30. a aad aad

a(S) FE an ve
‘TheBasks 3

Part S: Basic Geometry
39. Find the length of the unknown side inthe triangle below.

bat
40, Find the circumference and the area of a circle with diameter 10
inches.

41, Find the volume of the rectangular solid with length 10, height 2,
and wideh 4,

42. Find the distance ofthe line segment below and its midpoint.

Part 6: Applications

43, A specialty coffee shop wishes to blend a $6-per-pound coffee
with an $11-per-pound coffee to produce a blend that will sell for
$8 per pound. How much of each should be used to produce 300
pounds for the new blend?

44, An investor has $20,000 to invest. If part grows at an interest rate
ff 8 percent and the rest at 12 percent, how much should be
invested at each rae to yield 11 percent on the total amount
invested?

45. A boat takes 1.5 times as long to go 360 miles up a river than to
return. Ifthe boat cruises at 15 miles per hour instill water, what
is the rate of the current?
aed Sorter
(“Gy ae Me aew
12 anos tata ean an
Ebatesey
Me eons 15. nate
ee aemerteon
feeaieen
bine neem
Pease

16. 2340)22+0)-09- 029-0)
(ee thao 200 0

we
MT be he Be 2B Da 80S

Be sures

pa
18. opm 2e TPIS

wa
20, 950-0440 2 sean rd
Beem Wowen-m Becta
B.aatsaees-1He02) Te or-mucveee) — TB. game 7d

29, ras es2aysby 30. (V8 ah
ober fer
Gases

32. VPeevE
The Basis 5

nS) s-08-n6e
2». (3539) Fea)
Bierwes
pre
ae
0c Avo tadn oreo
angen 12.0 a9
ae SHB otecotee
oa aomeet ance

(44, are 2008 = 12000)
e+ r2a0000-) = 112008)

Ey Exponents

[As you should already be aware, exponents are a way of showing
repeated multiplication. For example, 2 (read “two cubed” of “two 0
the thd power”) means we multiply 2(2)(2) = 8. The 2is che base and
the 3 is the exponent, or power. The exponent tells us how many times
‘we use the base as a factor. So, = aaa). The reverse i also tue: we
ould say tha x(x)(x)2)(x) = (ead “x tothe fifth power"). There are
nine basic laws of exponents you should know for precalculus. As we
0 over these laws, we'll ask you to try some, then check your answers
‘with ours. There will be problems where you will have o apply more
than one of these laws. Generally you don't have to apply them in the
same order we have. There is no preset order of laws used for simplify-
ing exponents. Let's ge started.
PRECALCULUS

the bases are the same, add the

Example 3:
P2aF=32

Example 4:
(2a°bc*\(306*d) = 6a'b'c® Multiply the coefficients, add the
‘exponents.

Law 2:

Geax ‘When raising a power to a power, multiply the
exponents.

Example 5:

wren

Example 6:

vey"

Example 7:

QP a2 64

“The cis a constant. Ifa constant isin parentheses
with an exponent on the outside of the parenthe-
ses, the constant is also raised to that power.

Example 9: