, Theme I unit 1 . 1
Function #
Anything with multiple outputs - function
input ↳
I , output Only Real numbers
Input
Yd
= i e .
g. IS f(x) = >+ 1 a function !
Function = A =
Aci) ER is an input f(x)
y
=
Output = d YER is an output
Let
y . yzER so
ye
=
f(x) and
ye
=
f(2)
for same fixed ER
-
f(x) yz f(x)
y1
= =
=
x+ 1 = x+ 1
=
y
f function
Or : is a
a
-content -a+ 1 Inputs = Domain (x)
[vertical line test] Outputs =
Range (y)
&
*
y
⑧
e .
g
. h :
side
length
A = Area
&
ps
&
&
e , -
&
A 142581
& &
&
: A =
22
A =
f(b) =
12
↑ & 4
output function input
, Set Notation
[1 ,
2
,
3
3 Set contains 1 ,
2 .
3
- or
: Condition to be in Set
[x(xER]
belong
inset gives
3
condition
The set such that 3) is real number
among a
[x(xER ,
0 -x < 13
>
- including O , excluding I
Set such thats is and O < I
containing a real number
#
only use real numbers - don't need ER
↳.: [x(013
Interval Notation (x(a(x} (a ,
8)
e .
g Fix a ,
bER with a <b (xla(3 (a ,
x)
[x(ER ↓
,
a 1x1b3 -
[a ,
b] closed
not needed Interval Notation (x(x > a] [ -
D , a]
(laz(b] >
- [a b) , Half open (x(x(a]( - 0 , a)
Slab3 (a , b) open Gx/xER3 =
R (-0 , 2)
Spla(1b3 - (a ,
b] Half closed
⑧
--
G
-
↑
interval
&
Ray Straight line
, · ·
[a b] ,
R
· ·
A B
o - 0
(a b),
R
· ·
A B
· o
[a b),
R
· ·
A B
-
(a ,
b]
· R
·
A
⑧>
(a , x]
R
·
A
O &
(a , X)
0- 0
·
↓ db [
IR
Overlap :
o ·
Intersection
[a b]M(d ()
, ,
= (d , b]
: o union
Merge
(a b]U(d c)
. ,
=
(a ,
s)
Function #
Anything with multiple outputs - function
input ↳
I , output Only Real numbers
Input
Yd
= i e .
g. IS f(x) = >+ 1 a function !
Function = A =
Aci) ER is an input f(x)
y
=
Output = d YER is an output
Let
y . yzER so
ye
=
f(x) and
ye
=
f(2)
for same fixed ER
-
f(x) yz f(x)
y1
= =
=
x+ 1 = x+ 1
=
y
f function
Or : is a
a
-content -a+ 1 Inputs = Domain (x)
[vertical line test] Outputs =
Range (y)
&
*
y
⑧
e .
g
. h :
side
length
A = Area
&
ps
&
&
e , -
&
A 142581
& &
&
: A =
22
A =
f(b) =
12
↑ & 4
output function input
, Set Notation
[1 ,
2
,
3
3 Set contains 1 ,
2 .
3
- or
: Condition to be in Set
[x(xER]
belong
inset gives
3
condition
The set such that 3) is real number
among a
[x(xER ,
0 -x < 13
>
- including O , excluding I
Set such thats is and O < I
containing a real number
#
only use real numbers - don't need ER
↳.: [x(013
Interval Notation (x(a(x} (a ,
8)
e .
g Fix a ,
bER with a <b (xla(3 (a ,
x)
[x(ER ↓
,
a 1x1b3 -
[a ,
b] closed
not needed Interval Notation (x(x > a] [ -
D , a]
(laz(b] >
- [a b) , Half open (x(x(a]( - 0 , a)
Slab3 (a , b) open Gx/xER3 =
R (-0 , 2)
Spla(1b3 - (a ,
b] Half closed
⑧
--
G
-
↑
interval
&
Ray Straight line
, · ·
[a b] ,
R
· ·
A B
o - 0
(a b),
R
· ·
A B
· o
[a b),
R
· ·
A B
-
(a ,
b]
· R
·
A
⑧>
(a , x]
R
·
A
O &
(a , X)
0- 0
·
↓ db [
IR
Overlap :
o ·
Intersection
[a b]M(d ()
, ,
= (d , b]
: o union
Merge
(a b]U(d c)
. ,
=
(a ,
s)
