Calculus 1
Functions
1.
Part
^^
:&
2. Limits
1
Functions
:
lR={ real
wed , September 14,2022
} {
}
-
numbers
_
a
is
a
use
it
a
real number
,
3.
em
Derivatives
Integrals
4.
(i.
↳,
-1
=
i -1112
,
+ ≤ IR
,
A
we dont
is a
set of
)
numbers
↑
symbol
Let D
be
a
A function
exactly
✗ C-
of
set
f
subset
for
real numbers
with domain D
is
a
assigns
that
rule
to
✗
every
1.) f- 1×1=1
flxk.IR
one number, written as
3.) 1-1×1=2×+1
Examples
ED
D
d
Dom
,
(f)
=
IR
a
function
constant
eg
↑
element of
We
eg
D= Domain (f)
write
The
tlx) is
number
Graphs
called
,
the
off
:{
IR
( x,y )
set of all
every ix. y ) is a point
( 2,3)
C- 1,1)
,
,
pairs of numbers
(f)
#
=
,
×,y )
✗
C- Dom /f) ,
"""""
-1
,
!
23
=
2-
(
=/
( × , tix))
✗ c-
×
}
Dom (f)
graph
is
a
curve
the
in
plane
1- (21--2,1-13)=3
,
-
if
×
f- (2) = 5. 1- (3)
Dom /f)
,
=
eg.tl 3)
it
5.)
)=¥
f- (x
,
Dom
(f)
=
{
✗ c-
IR
✗
}
=/ 0
f- (01=0
=
1
,
C- (2)
=t
,
1- (3) =
}
× >
Dom
(f) IR
=
I
-
function
4
=
-
,
,
1- C-
f- (1) =/
2) =3
1- (2)
,
fl
-
,
1)
=
2
4
=
.
A
1.)
1-1×1=1
2.)
-
1- ( x) =
^
×
1
The
,
graph determines
the
•
function
✗
3.) 1-1×1=2×+1
The
^
4.)
-
f- (x) =
✗
2
^
.
Dom
=
Of
the
The
graph
(f)
f- (x)
value
is
the
above
graph
height
×
.
&
&
5.)
tlx)=¥
6.)
a
1-1×1=1
'
-
✗
×
it
✗
≤
-
•
but
not
What
are
is
all
a
curve
curves
× >
in the
are
plane
graphs
.
t
2
if
-1
What
&
.
The
vertical
A
curve
of
a
line
in
function
intersects
Example
acceptable
are
the
not
graphs and
?
test :
the
if
Cartesian
and only
graph
more
no
than
in
the
vertical
once
graph
line
.
A.
•o•
NOT
if
plane
.
••
~:
a
function
=
>
IR
✗ ≤y
,
1×2
y=f( )
3-
The
,
""" "° "
.
1- ( x)
IR
1- (01--0,1-11)=1,1-127--4,1-13)=9
IR
=
eg 1- (1)
piecewise
•
-2
f- (D) =L , f- (1) =3
reciprocal functions
I
-3
Dom (f)
,
=
1- (2) =L
,
1- (01--0,1-11)=1
6)
•o
tlx)=x
+"
( 0,0)
Graph
-
2)
/
}
,yElR
in the plane
•a•
-
×
.
Dom (f)
linear function
4.) tlx)=x2
of ×
of functions
Cartesian plane
1- (1) = 1
,
off
domain
value
the
f- ( O) -- 1
.
.
,
Yes
NO