College Algebra Fourth Edition.pdf

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EXPONENTS AND RADICALS
a
m
a
n
Óa Ô
ÓabÔ
a
1
n
n
œ
ab
m n
DISTANCE AND MIDPOINT FORMULAS
n
a
m
a
mn
n
a
m
a
n
a
a
b
n
n
a
m
Distance
between
P
1
Óx
1
,
y
1
Ô
and
P
2
Óx
2
,
y
2
Ô:
d
Midpoint
of
P
1
P
2
:
n
!œ
a
@
m
n
ab
n
œ
a
n n
!@
a
m n
n
1
a
n
a
n
b
n
n
œ
a
m
œÓx
2
x
1
Ô
2
x
2
y
1
,
Ó
y
2
y
2
2
y
1
Ô
2
!
x
1
2
@
y
2
x
2
y
1
mx
y
b
y
1
x
1
mÓx
b
1
x
1
Ô
LINES
Slope of line
through
P
1
Óx
1
,
y
1
Ô
and
P
2
Óx
2
,
y
2
Ô
Point-slope equation
of line
through
P
1
Óx
1
,
y
1
Ô
with slope
m
Slope-intercept equation
of
line with slope
m
and
y-intercept b
Two-intercept equation
of line
with
x-intercept a
and
y-intercept b
m
y
y
x
a
b
2
are
m
1
m
1
m
2
1
m
2
n
n
œ
a
œ
b
a
b
œ
a
n
œ
b
n
mn
œ
œ
a
nm
œ
œ
a
mn
œ
a
SPECIAL PRODUCTS
ÓA
ÓA
ÓA
ÓA
BÔ
2
BÔ
2
A
2
A
2
2AB
2AB
3A
2
B
3A
B
2
B
2
B
2
BÔ
3
BÔ
3
A
3
A
3
3AB
2
3AB
2
B
3
B
3
The lines
y
m
1
x
b
1
and
y
m
2
x
Parallel
if the slopes are the same
Perpendicular
if the slopes are
negative reciprocals
LOGARITHMS
y
log
a
x
means
a
y
x
0
x
a
log
a
x
log
a
a
FACTORING FORMULAS
A
2
A
2
A
2
A
3
A
3
B
2
2AB
2AB
B
3
B
3
ÓA
B
2
B
2
ÓA
ÓA
BÔÓA
ÓA
ÓA
BÔÓA
2
BÔÓA
2
BÔ
BÔ
2
BÔ
2
AB
AB
B
2
Ô
B
2
Ô
log
a
a
x
log
a
1
x
1
QUADRATIC FORMULA
If
ax
2
bx
c
0, then
x
b
œ
b
2
2
a
4
ac
Common and Natural Logarithms
log
x
log
10
x
ln
x
log
e
x
Laws of Logarithms
log
a
AB
log
a
log
a
A
log
a
A
C
log
a
A
log
a
B
log
a
B
INEQUALITIES AND ABSOLUTE VALUE
If
a
If
a
If
a
If
a
If
a
b
and
b
b,
then
a
b
and
c
b
and
c
0, then
x
x
x
a
a
a
means
x
means
means
x
a
a
a
x
or
or
x
a.
x
a.
a.
c,
then
a
c
b
c.
c.
cb.
cb.
!
A
@
B
log
a
A
C
0, then
ca
0, then
ca
Change of Base Formula
log
b
x
log
a
x
log
a
b
SOME FUNCTIONS AND THEIR GRAPHS
Linear functions
y
Exponential functions
y
fÓxÔ
a
x
y
Ï=a˛
0<a<1
fÓxÔ
mx
b
y
Ï=a˛
a>1
1
1
x
0
b
Ï=b
x
Ï=mx+b
m≠0
b
x
0
x
Logarithmic functions
y
Ï=log
a
 x
a>1
fÓxÔ
log
a
x
y
Ï=log
a
 x
0<a<1
Power functions
y
fÓxÔ
x
n
y
0
1
x
0
1
x
Ï=≈
Ï=x£
x
y
y
x
Absolute value function
y
Greatest integer function
y
1
Ï=x¢
x
Ï=x∞
x
_1
1
x
1
1
x
Ï=|x |
Ï=“x ‘
SHIFTING OF FUNCTIONS
Root functions
y
fÓxÔ
n
œ
x
Vertical shifting
y
y
y=Ï+c
y=Ï
c
x
x
c
y=Ï-c
x
c>0
Ï=œ∑
x
Ï=£ x
Ϸ
Reciprocal functions
y
fÓxÔ
1
x
n
y
Horizontal shifting
y
y=f(x+c)
y=Ï
y=f(x-c)
c
c
x
Ï=
1
x
Ï=
1
≈
x
x
c>0
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