Hungerford T.W., Shaw D.J. Contemporary Precalculus: A Graphing Approach
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Distance Formula
Midpoint Formula
Slope of nonvertical line Equation of line with Equation of line with slope m
through and
slope m through and y-intercept b
y mx by y
1
m1x x
1
2
y
2
y
1
x
2
x
1
1x
1
, y
1
21x
2
, y
2
21x
1
, y
1
2
a
x
1
x
2
2
,
y
1
y
2
2
b
Midpoint M of segment PQ
21 x
1
x
2
2
2
1y
1
y
2
2
2
Length of segment PQ
b
a
c
b
h
Change of Base Formula
log
b
v
ln v
ln b
r
Natural Logarithms Logarithms to Base b Special Notation
For v, w 0 and any u, k: For v, and any u, k: ln v means
means
Geometry
The Pythagorean Theorem Area of a Triangle Circles
Area pr
2
Circumference 2pr
Diameter 2rA
1
2
bhc
2
a
2
b
2
log
b
1v
k
2 k1log
b
v2ln 1v
k
2 k1ln v2
log
b
a
v
w
b
log
b
v log
b
wln
a
v
w
b
ln v ln w
log
b
1vw2 log
b
v log
b
wln 1vw2 ln v ln w
log
10
vlog vlog
b
v u means b
u
vln v u means e
u
v
log
e
vw 7 07
The Quadratic Formula
are the solutions of . ax
2
bx c 0
x
b ± 2b
2
4ac
2a
Algebra
Equations and Graphs
The solutions of the equation are
the x-intercepts of the graph of y f 1x2.
f 1x2 0
Exponents
1c 02c
r
1
c
r
1d 02
a
c
d
b
r
c
r
d
r
1cd2
r
c
r
d
r
1c
r
2
s
c
rs
c
r
c
s
c
rs
c
r
c
s
c
rs
Multiplication and Factoring
u
3
v
3
1u v21u
2
uv v
2
2
u
3
v
3
1u v21u
2
uv v
2
2
1u ; v2
2
u
2
; 2uv v
2
u
2
v
2
1u v21u v2
M
P
Q
(x
1
, y
1
)
(x
2
, y
2
)
Slope = m < 0
f(x) = mx + b
Slope = m > 0
f(x) = mx + b
x
y
Linear Functions
x
y
Identity Function f(x) = x
x
y
Constant Function f(x) = b
x
y
b
x
y
Cube Function f(x) = x
3
x
y
Square Function f(x) = x
2
x
y
Square Root Function f(x) = x
Greatest Integer Function f(x) = [x]
Absolute Value Function f(x) =
⏐
x
⏐
x
y
x
y
1
1
f(x) = x
n
(n even) f(x) = x
n
(n odd)
x
y
Reciprocal FunctionsPower Functions
x
y
x
y
x
y
f(x) =
1
x
f(x) =
1
x
2
f(x) = b
x
(b > 1) f(x) = b
x
(0 < b < 1)
Exponential Functions
1
x
y
x
y
1
1
Logarithmic Functions
x
y
x
y
1
f(x) = log xf(x) = ln x
Catalog of Basic Functions
ContinuesS
Rectangular and Parametric Equations for Conic Sections
Circles Ellipse Parabola
Center (h, k), radius r Center (h, k) Vertex (h, k)
1x h2
2
4p1y k2
1x h2
2
a
2
1y k2
2
b
2
11x h2
2
1y k2
2
r
2
k
h
k
h
k
h
y r sin t k
10 t 2p2
x r cos t h
y b sin t k
10 t 2p2
x a cos t h
(t any real)
y
1t h2
2
4p
k
x t
Parabola Hyperbola Hyperbola
Vertex (h, k) Center (h, k) Center (h, k)
1y k2
2
a
2
1x h2
2
b
2
1
1x h2
2
a
2
1y k2
2
b
2
11y k2
2
4p1x h2
k
h
k
h
k
h
(t any real)
y t
x
1t k2
2
4p
h
y b tan t k
10 t 2p2
x
a
cos t
h
y
a
cos t
k
10 t 2p2
x b tan t h
Catalog of Basic Functions (continued )
2π
−2π
1
f(t) = sin t
−1
t
y
2π
−2π
1
−1
t
y
2π
−2π
t
y
f(t) = cos tf(t) = tan t
Trigonometric Functions
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Contemporary Precalculus
A Graphing Approach
5e
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A Graphing Approach
5e
THOMAS W. HUNGERFORD
Saint Louis University
DOUGLAS J. SHAW
University of Northern Iowa
Australia • Brazil • Canada • Mexico • Singapore • Spain
United Kingdom • United States
Contemporary Precalculus
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STUDENT EDITION:
ISBN-13: 978-0-495-10833-7
ISBN-10: 0-495-10833-2
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Contemporary Precalculus: A Graphing Approach, Fifth Edition
Thomas W. Hungerford, Douglas J. Shaw
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To the memory of my mother and my aunts,
Whose presence in my life has greatly enriched it:
Grace Parks Hungerford
Irene Parks Mills
Florence M. Parks
Ellen McGillicuddy
❖❖❖
For my daughter Francebelle Shaw, whose response to
“Stop being so cute, I seriously can’t take it”
was to give me a big smile and kiss me on the tip of my nose.