Basic Sin Cos Tan Chart

Zeros of polynomials:
The solutions to
2
0ax bx c
are
2
4
2
b b ac
x
a
If
( )P x
is a polynomial with leading coeDcient a and constant term c, then any rational zeros must be of
the form
p q
where p is a divisor of c and q is a divisor of a.
Exponents and logarithms:
log
x
b
b y y x
A.
x y x y
b b b
log log log
b b b
x y xy
B.
x
x y
y
b
b
b
log log log
b b b
x
x y
y
C.
y
x xy
b b
log log
y
b b
x y x
D. If
x y
b b
or if
log log
b b
x y
, then
x y
E.
log
x
b
b x
and
b
log x
b x
F.
10
log logx x
and
ln log
e
x x
G.
log
log
log
c
b
c
a
a
b
Transformations of graphs:
A.
( )y f x a
is the graph of
( )y f x
shifted horizontally
a
units (to the right if
0a
and to the
left if
0a
)
B.
( )y f x a
is the graph of
( )y f x
shifted vertically
a
units (up if
0a
and down if
0a
)
C.
( )y af x
is the graph of
( )y f x
stretched or shrunk vertically by a factor of
a
(stretched if
1a
and shrunk if
0 1a
)
D.
( )y f ax
is the graph of
( )y f x
stretched or shrunk horizontally by a factor of
a
(stretched if
0 1a
and shrunk if
1a
)
E.
( )y f x 
is the graph of
( )y f x
reGected over the x-axis
F.
( )y f x
is the graph of
( )y f x
reGected over the y-axis
Sequences and series:
Arithmetic:
1n n
a a d
;
1
( 1)
n
a a n d
;
1
2
n
n
n a a
S
Geometric:
1n n
a a r
;
1
1
n
n
a a r
;
1
(1 )
1
n
n
a r
S
r
;
1
, 1
1
a
S r
r
Special products and factoring
Sum/diJerence of two cubes:
3 3 2 2
3 3 2 2
a b a b a ab b
a b a b a ab b
Basic graphs:
y x
1
y
x
y x
n
y x
, n even
n
y x
, n odd
x
y a
,
1a
, 0 1
x
y a a
log , 1
a
y x a
log , 0 1
a
y x a
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