Math 27 Pre Calculus Class Notes

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