Math 27
Pre-Calc Algebra
,.)
2 Finding Domain
·
Finding the domain
~
of f(x)
never :
by 0 ,
never reg
interval
4) Find the domain notation set notation
a f(x) = 2x2 + 3 Domain :
1-5 0) ,
or ExIXisR3
& "the
polynomial fxr set of all X where
"
X is all real #s
g(x) = (x(x 73
:
=
b .
Domain
o r
↑ rational fxn ( 0
,
7) u(7 0 ,
1st solve domain =
o
7 7
umu
X - = 0 so x
=
closed
y ~ ↓ open
c .
g(x) = 5x4 Domain : [4 0) ,
or Ex/X143
↑ radical fxn
~ Mus
solve radicand I O
X
-
420 so x14
if flip
* <
or -
by neg .
# ,
have to
inequality
d .
h(x) =3 +
Domain :
(3 0) ,
or
Ex(x1 33 -
need x + 310 so x] -
3
also
"I d In
need x + 3 =
0soX = -
3
,. 2 Graphs of fxn
2
·
fxn IE
a curve is a
any
vertical line intersects curve
just once
↳ "each
X
get just one
y"
1) a Is it a fxn ? Yes ! 2) f(x) =
.
.
a is point (3 , 3) on graph f(x)
↑
=
&
6
X yes (3 6), ,
is on
graph f(x)
--
4
Y
.
b For X = -2 ,
what is f(x) ?
(-0
= -
D: 3) x-axis
,
-( 2) =
(2 1) ,
R :
[- 4 0) , y-axis
↳
(y(y = -
43
b Is it a fxn ? Yes ! c .
If f(x) =
3 what is X ?
. ,
-
·
S
18
>
(
X
.
d Find Domain of f(x) can't have O in denom
Y
X -
2 =
0 so X =
2 exclusion Ex/x = 23
D: M or
( -
0
00) ↑
set denom = O
or
( 2)u(2 a)
,
-
-,
E53 just
,
R: 5
2 .
Is it a fun ? No !
M
X
is
~
Y
D : E103
R: ( -
0
,
3)
, .3
2 Properties of Exns
·
Defn : f(x) is an even fxn if f) -x) =
f(x)
↳
graphically ,
all even fxns have
symmetry w . r .
t
y
axis
to
verify fun is a even ,
we evaluate f(x) +
simplify to see if it =
f(x)
#
: =
(x2) is even
fxn : = x3
y
an
y
-
3
%
X=
(2 , 8) y
(4) (4)2
2
y
= =
y
=
-8)
·
(2 ,
W
·
Defn : f(x) is an odd Exn if 5( x)
-
= -
f(x)
graphically all odd fxn have
symmetry w r
. .
t the
origin
1) verify algebraically if fxn is even
,
odd or neither
a f(x) =
3x4 -
8 *
neg
#even =
pos
#old =
A
.
,
neg neg
5( x) - =
3) x)4-
-
8
=
3x4 -
8
·
f(x)3x4-8 : f(x) is even
b . f(x) =
xY -
8x
f( x) =
( x)4 8( x) h(x) () = od
- -
- -
- = -
=
x4 +
8x = x" 8x-
neither even or odd
Defn :
fxn interial I if for all where
a is
increasing on an
, ,
X , Xz ,
are in I
+,, X2 N
f(x ) ,
<
5(xz
· 1X ,
x)
*
y gets bigger as
you
move
right * ~
I
Pre-Calc Algebra
,.)
2 Finding Domain
·
Finding the domain
~
of f(x)
never :
by 0 ,
never reg
interval
4) Find the domain notation set notation
a f(x) = 2x2 + 3 Domain :
1-5 0) ,
or ExIXisR3
& "the
polynomial fxr set of all X where
"
X is all real #s
g(x) = (x(x 73
:
=
b .
Domain
o r
↑ rational fxn ( 0
,
7) u(7 0 ,
1st solve domain =
o
7 7
umu
X - = 0 so x
=
closed
y ~ ↓ open
c .
g(x) = 5x4 Domain : [4 0) ,
or Ex/X143
↑ radical fxn
~ Mus
solve radicand I O
X
-
420 so x14
if flip
* <
or -
by neg .
# ,
have to
inequality
d .
h(x) =3 +
Domain :
(3 0) ,
or
Ex(x1 33 -
need x + 310 so x] -
3
also
"I d In
need x + 3 =
0soX = -
3
,. 2 Graphs of fxn
2
·
fxn IE
a curve is a
any
vertical line intersects curve
just once
↳ "each
X
get just one
y"
1) a Is it a fxn ? Yes ! 2) f(x) =
.
.
a is point (3 , 3) on graph f(x)
↑
=
&
6
X yes (3 6), ,
is on
graph f(x)
--
4
Y
.
b For X = -2 ,
what is f(x) ?
(-0
= -
D: 3) x-axis
,
-( 2) =
(2 1) ,
R :
[- 4 0) , y-axis
↳
(y(y = -
43
b Is it a fxn ? Yes ! c .
If f(x) =
3 what is X ?
. ,
-
·
S
18
>
(
X
.
d Find Domain of f(x) can't have O in denom
Y
X -
2 =
0 so X =
2 exclusion Ex/x = 23
D: M or
( -
0
00) ↑
set denom = O
or
( 2)u(2 a)
,
-
-,
E53 just
,
R: 5
2 .
Is it a fun ? No !
M
X
is
~
Y
D : E103
R: ( -
0
,
3)
, .3
2 Properties of Exns
·
Defn : f(x) is an even fxn if f) -x) =
f(x)
↳
graphically ,
all even fxns have
symmetry w . r .
t
y
axis
to
verify fun is a even ,
we evaluate f(x) +
simplify to see if it =
f(x)
#
: =
(x2) is even
fxn : = x3
y
an
y
-
3
%
X=
(2 , 8) y
(4) (4)2
2
y
= =
y
=
-8)
·
(2 ,
W
·
Defn : f(x) is an odd Exn if 5( x)
-
= -
f(x)
graphically all odd fxn have
symmetry w r
. .
t the
origin
1) verify algebraically if fxn is even
,
odd or neither
a f(x) =
3x4 -
8 *
neg
#even =
pos
#old =
A
.
,
neg neg
5( x) - =
3) x)4-
-
8
=
3x4 -
8
·
f(x)3x4-8 : f(x) is even
b . f(x) =
xY -
8x
f( x) =
( x)4 8( x) h(x) () = od
- -
- -
- = -
=
x4 +
8x = x" 8x-
neither even or odd
Defn :
fxn interial I if for all where
a is
increasing on an
, ,
X , Xz ,
are in I
+,, X2 N
f(x ) ,
<
5(xz
· 1X ,
x)
*
y gets bigger as
you
move
right * ~
I
