Math
Sets
theory
: Unordered collection
of elements ,
e . .
g
22 ,
1
, 39 21 ,
,
1
,
2
,
3 1
, , 34
N natural nambers e 21 2 3
, 4.... 3
g
= .
,
.
, ,
2..., element
*=
integere . ..
e 2
, 0 1 3,
3 of
-
g
-1
, , , , ,...
1
① =
rational numbers ,
s .
g
.: Sm gelotdon ENNY
↑
,
L; -
2 , 25 4 , 5
; ;..
real numbers all rationaland virational
... 25
IR= ,
numbers ,2 ,
T , ...
23 5,
,
=
Complex numbers
g Rabis a beR 14 23 + 21 5+ 5 .....
2
e . . i =
, , , , ,
INc XL QCIRC K
1
↳ c
c sube et that isn't identical
proper
=> =
- = subset with identical members
element
t =
of
V = union between
iet ,
Ex : xeAorxE BY S g ,
.
.. 21 ,
2
,
33092 3 43 21 , ,
=
,
2
,
3, 44
= intersection between sets Ex xeAomoxe BY e 21 2 24 r22 3 43 22 34
g
: .. , , ,
=
,
, , ,
.
relative
1 =
complement , BLA =
RX : xC Bamdxz AY ,
.
l
g 22
.:
,
3 ,
43141 33 22 4} ,
=
,
Interval notation :
[a, b] = 2x E(R(a xx - b} (a ,
b2 =
(x t(R(a xx(b} 5 -
x ,
b] :
+EIR1 x ≤ bY
Ja, b( = (x = R(a < x < b} Jouib :reIRlorsrafy ]
t ∞ L = $ E 1 R/ × 300 I
Polynomials of 2nd degree
{…lh
tbysc
ofsymmetry Et
'
Y
= Qx
Top + oxxi : x =
↳dicriminants d b ?
nas intersection withx Sx (x 0) ; (x 0)
wauwob
= : :
/
: _
2
1
.
.
intersection
withy Sy : : 10 , c)
Polynomiidofologree 0 hghes ,
Homer : oon
a.
oim .
bna
?
äbe
f
-
a
ㆀ
bo
on
long division : e .
g
.:
3+
115x-
a .
An but to 0
'
, Functions :
domain set
of allpoints which it defined value over is
range-set of allvalues whichit attains cy values
Constant
function fix horizontal hie
-
infut and output the constant c it : = c
,
no ,
so is a
lucas function f x multiplier input by and addic the graph line
↑
: =
mxxc ,
no is a
,
identity function fsx = special oflinearfunction 1 : = X
,
case Im = c =
quadratic function fix axbxxc the :
,
is a
polynomial of zo degree , graph in a parabolas cumbe at o
polynomial f(x)
*
*
*+ 0nX : =
anX +.. .
+ 0
,
x + ax +
01
signumfunction fsx gn egn(x)
. = s (x) ,
=
2, y *?
so
trigonometric function fx in (x) : = , ...,
is a
repetitive graph with period and a an
amplitude ,
Cos O + si20 =
exponential function fsx b
*
: =
logarimic function loge y if b* . x z x le .
g
..
log z 81z3 = 223 = 81 =
loge (x yl loge logesy
.
=
x .
transformations offuntions
zfirjsromylitiols {
-,
:
: nns Iwew " whiotyou seerimhrtyos
mite
olile
e
tion
mulliplyiojthefunilin ya comto al 3f z
-
: 1 I
"WYSIOYW"-what see is opposite you write
-translation
:
you
adding a constant to the
function fix fix up = + 21
↳ Look
,
+ 2
or down
( + 3) x(X 2)
=
-
=) R
Vertecfumelion fixkr thrtc +- _1
製
:
'
sst - hitk = o ( ) '
tc
Wircle :
Center alxa, radiu
yal ,
>
-
: : r
)
(5 × oa ' t yo を
(y
-
-
) =
Ellipse :
愕)(=^
wide
if 0 it's
'
↳ c= = a
d =
elliper is vertical
ccd = ) i
"horizontal
Hyperbolos :
べ
i
k (k > d
^
Type 1 (X a)
(y b)
:
- -
=
^
k (h > d
>
Type 2 (x-al2
(y l)"
:
=
-
μ
Sets
theory
: Unordered collection
of elements ,
e . .
g
22 ,
1
, 39 21 ,
,
1
,
2
,
3 1
, , 34
N natural nambers e 21 2 3
, 4.... 3
g
= .
,
.
, ,
2..., element
*=
integere . ..
e 2
, 0 1 3,
3 of
-
g
-1
, , , , ,...
1
① =
rational numbers ,
s .
g
.: Sm gelotdon ENNY
↑
,
L; -
2 , 25 4 , 5
; ;..
real numbers all rationaland virational
... 25
IR= ,
numbers ,2 ,
T , ...
23 5,
,
=
Complex numbers
g Rabis a beR 14 23 + 21 5+ 5 .....
2
e . . i =
, , , , ,
INc XL QCIRC K
1
↳ c
c sube et that isn't identical
proper
=> =
- = subset with identical members
element
t =
of
V = union between
iet ,
Ex : xeAorxE BY S g ,
.
.. 21 ,
2
,
33092 3 43 21 , ,
=
,
2
,
3, 44
= intersection between sets Ex xeAomoxe BY e 21 2 24 r22 3 43 22 34
g
: .. , , ,
=
,
, , ,
.
relative
1 =
complement , BLA =
RX : xC Bamdxz AY ,
.
l
g 22
.:
,
3 ,
43141 33 22 4} ,
=
,
Interval notation :
[a, b] = 2x E(R(a xx - b} (a ,
b2 =
(x t(R(a xx(b} 5 -
x ,
b] :
+EIR1 x ≤ bY
Ja, b( = (x = R(a < x < b} Jouib :reIRlorsrafy ]
t ∞ L = $ E 1 R/ × 300 I
Polynomials of 2nd degree
{…lh
tbysc
ofsymmetry Et
'
Y
= Qx
Top + oxxi : x =
↳dicriminants d b ?
nas intersection withx Sx (x 0) ; (x 0)
wauwob
= : :
/
: _
2
1
.
.
intersection
withy Sy : : 10 , c)
Polynomiidofologree 0 hghes ,
Homer : oon
a.
oim .
bna
?
äbe
f
-
a
ㆀ
bo
on
long division : e .
g
.:
3+
115x-
a .
An but to 0
'
, Functions :
domain set
of allpoints which it defined value over is
range-set of allvalues whichit attains cy values
Constant
function fix horizontal hie
-
infut and output the constant c it : = c
,
no ,
so is a
lucas function f x multiplier input by and addic the graph line
↑
: =
mxxc ,
no is a
,
identity function fsx = special oflinearfunction 1 : = X
,
case Im = c =
quadratic function fix axbxxc the :
,
is a
polynomial of zo degree , graph in a parabolas cumbe at o
polynomial f(x)
*
*
*+ 0nX : =
anX +.. .
+ 0
,
x + ax +
01
signumfunction fsx gn egn(x)
. = s (x) ,
=
2, y *?
so
trigonometric function fx in (x) : = , ...,
is a
repetitive graph with period and a an
amplitude ,
Cos O + si20 =
exponential function fsx b
*
: =
logarimic function loge y if b* . x z x le .
g
..
log z 81z3 = 223 = 81 =
loge (x yl loge logesy
.
=
x .
transformations offuntions
zfirjsromylitiols {
-,
:
: nns Iwew " whiotyou seerimhrtyos
mite
olile
e
tion
mulliplyiojthefunilin ya comto al 3f z
-
: 1 I
"WYSIOYW"-what see is opposite you write
-translation
:
you
adding a constant to the
function fix fix up = + 21
↳ Look
,
+ 2
or down
( + 3) x(X 2)
=
-
=) R
Vertecfumelion fixkr thrtc +- _1
製
:
'
sst - hitk = o ( ) '
tc
Wircle :
Center alxa, radiu
yal ,
>
-
: : r
)
(5 × oa ' t yo を
(y
-
-
) =
Ellipse :
愕)(=^
wide
if 0 it's
'
↳ c= = a
d =
elliper is vertical
ccd = ) i
"horizontal
Hyperbolos :
べ
i
k (k > d
^
Type 1 (X a)
(y b)
:
- -
=
^
k (h > d
>
Type 2 (x-al2
(y l)"
:
=
-
μ
