NA�t: --------KEY----------
R.evtew for ChApter 3 ,est
1>0Lt1 �o�LAL & Rational
Fw.�t>tto�s
Circle the Pol nomial Functions.
3.
2.
Y=-2x3 -)(+x.+ 1
y = 3x5 + 2x2
:)xf+ 6
y = (x + 4) (x - 3) (x + 1 )
Find the End Behavior
Function
5
f(x) = 4x3 -2x2 -3x+ 6
6
g(x)=x2 (x-5)(x+3)
7
g(x) = -6(x + 1 )2 (x - 3)
8
J(x)=-3x 4 +4x3 +7
Degree
3
+/
'-I
-3
10.
End Behavior
x�-oo, f(x) � - a,()
x�oo, f(x)� c:I)
-+ '-/
tf
3
Find all intercepts.
9.
Find ALL the intercepts of:
f (x) = (x - 2) (x + 3) (x - 1 )2
Lead Coeff.
x�-oo, f(x) � t:P
x�oo, f(x)� 00
-&
x�-oo, f(x) � fy)
x � oo, f(x)�-oO
x�-oo, f(x) � - <)()
x�oo, f(x) � - .tJO
Find ALL the intercepts of:
f (x) = x2 (x + 5) 2 (x + 2)
z.
(o•, o)
O :{x-2-)(K+?){x-1Y- (!, ) o � x (xrs) (xti-)
:::o (-� o)
o)
xt�
f�
:::-o
xfs
/
=x::.o
o
x-1
:01
;xta
x-1-::0
=
o)
-Z ft.l o)
x
5
x:{11
J
=)(
-.3
=X :, 2- X .
(o,,-�)
.,_
1..
2
(Ot2--)
)
t-5
(o
O
:
..!j
j "(D-Z){Ot-3){o-J)
0 {15) .,_{i-)
.:j = {-2) (?J) (-it
=0
� -t-) � I)
'-
o
I
.!f'·
Given the information provided, create a polynomial function in STANDARD FORM.
Degree: 4
11. Zeros: 3 {multiplicity 2)
-1 {multiplicity 2)
.j = (')(-8)2...(x+-1YJj = ('l(-?J)(x-o){x+!')(t-x+1)
rx�-3x-.3xf-Cl)(x: f-X+xH)
=-
,J::
::J
2...
t- -tt;x -t-61 x t.. +/Bx
)(ft:(){
)(
+-2-X-f-/)
1z.x
1-x3·
><2.+
3
({)
Ji :: X'" + 2 x
'L
'I
Function: j = x -LJ x'� - 2-.'x' + 12-X +-1
12.
�Z--�
Zeros: 3, -1, 2i
Degree: 3
t-1
This problem was replaced in class.
·z..
(x-3){x+-1){x-i-i)(x�zt)
::
J = {x z...-ox +->< -?J){x -z..-))4+-;,{x-'i, )
J " (x- -z.x-o)(x - '1{-i))
J
1:
i.
2..
i..
+'-1)
{x
- {x.2...-zx -3)
2- -1-x ? -8x -3x 2- -1 z
x
x"' +'f
Function:
jj= X 1 -tx�+X 2--flX -12....
Determine the zeros, multiplicity at each zero, and whether the graph bounces or
crosses at each zero.
13. g(x)=x(5x-2)2 (x+18)
14. f(x)=x2 (x+3)(x-4)3
Zeros:
0
Mult:
I
B/C:
t
%
28
-)8
Zeros:
I
Mult:
�-
*there may be fewer than 4 zeros
0
J_
-3
I
4
.3
B/C:
*there may be fewer than 4 zeros
Findin zeros of f x .
21. Given x = -2 is a solution of f(x) = x3 + 2x2 + 5x + 10, find all real number solutions.
-2..11 t
_ J; -2O
I
/0
-10
6
0
5
0
1+--D >< -t-0)
lx
(
)
2r
x:
{
-f'{x) =
-f'tx-)
22.
= {x+i.-) (x:
'L-
+-5)
x+2- = o
x:. -z_
jx= -2
j
f(x) = x3- 9x2 + tox-213 Find all zeros, provided that one zero is 5.
x=
-t'f
±
{'-1) 1--4(1){
2-(1)
x � '-/ ±. J/&;-2-0
.;
23.
�
.
x=
..
2--
'f d:. J-4
z_
Zi
X =- t./ ±
2X = Z±. i
f(x) = x3- 1Ox2 + 29x- 26. Find all zeros given that (x- 2) is a factor of f(x).
tf I
-.j/
I
-10
2-
-8
1-'t
-1,
-2-b
��
0
13
v
-Fcx) = (x-z){x -8x +-1'3)
1-
'7 2... b � 2;-e..rc .
X�
'Z-t� :!:.. f�) -'-f(t){ I )
J_ (t)
X =- 8 ±
x�
f;
J� '-I t-.
±J 12-
X =- 8 ±Ff[§
2-
5 2.
24.
-J
E
List the possible rational zeros of the polynomial function.
f(x) = x4-x3 + 3x2 + 4x- 15
Possible Rational Zeros:
25.
±
l
[ J, 3, 51 !'5 I
= 3x3 + 4x2 + x - 1O
�
15
Possible Rational Zeros:
26.
/0
r
;r
;r
1
�
l�T
r 1 /) � !i ,
- l 1J ..3 � �1 � � 5L � � I'0 3
+
I
�
List the possible rational zeros of the polynomial function.
f(x)
I
1- � ..3
10J
G
/0
f1Yl
f(x) = 2x3 + 3x2-39x - 20
t ,, ( 1., � � t '°' lD]
±
.t
1 - 2-0
B
o
t-/ -/ w B
z,o_ v/
Jf'-1
o
·5
JI
J_
-i+11 x �'? )
(zx
)
�4
-Frx) =-(x
.f
( x: -,; {x-'-f)
(ix +I )(x +6)
·� x = 41 -1/2, -5
= f(x) = 2x4 + x3 + 3x2 + 2x-2
f(x)
z7.f
±�
l 1I l
'Z-)
-I 2..
.3
I
.. . J; -t I
2- -., Lj
·. Jr I a
· 2- o· . '-f.
i
.
1-­
-Lf
-22..
o v-" o
'+ ox +-'-I)
ix
(
Y'
(x-i
I)
(x:+
=-Frx)
.
'
,-
I
:
'
.
'
-2 -2J ' > I
2-
� 2-
2-
2> I
1 �z
2--
t(x-i_=-o)
-J == 0
2
0
X (X +-ZX- ?J) >
lx 2--5x-3 � O
{tX'rO (x -3) �o
X= -f 3
@
]
e
;rs-�
- 3
z,.
f iJ a]
38.
x (x+ o){x-1) > o
X-:::.. 01
.·
(-)(-) = + � I �
.. - I :
0 : (+) (-) ;
X =- J J
1-
x :.
)(+-
x+ 12 < 7 .
ff-7< a
rx +-11=.)(
ca)}
2
2-.
�,
::::t c;,r
<
-2
:
(
+
J(
-r
J
�FJ
?- I J'""
)(+)
�
Ii
'A-tRf
40.
. (x-2)
x 2 -1
-
0
2
x -l=O
X =- I
i-
x =-±.. I
r® (f)
t � .. 7
2I
-------:-.
0: (-
2- : (:t-)(+)
«>) -1) V ( IJ 00)
G
-, : (�)�-t- 4 1.
I:
>
-Lf : (- )(-) ( )
-I : lr;J(+ )( )
(+)(+-)( )
±:
2: (+-)(+)( )
'
(x-t) � 0
\c xt..+1 =-O
I
'.!>
f
(B
ft5
[�oo,o)v (11
1-J :(H(+) =-+
x4 > 1
)( =--I
-8/ I
0
-�
-
X -I > 0
(x�J){">C+I) >D
'l0
(x-1 )(><+ I) {x -r 1) "?
4
x3 + 2x2 - 3x > O
37.
}2
'
r-x-J_
x-z.
f!-J -
< 3/-9
2.
.3x-C/
�
(x-a)Cx-�) < 0
eo
(:txJ o) v (31 4)
{x:-Z)(�X-1)
- '5)
L-JAQI
.;J_Ar:::°I
�A
. {4-)
c+)=_
o:(-)
I �: ( + ) - +
.�
(-r)
3 : ff--) ::.
o
3.'5: (�f->= 3)(-'t - 2.. (x:-2,) < o
x
(x-z)(o'x�J
l
x 2-1x+rL � 0 5. C+(+)(+
) .
x
Jx-1-z:x+ C/ � a
- 7X < 0
&-) =-+
-2· -
(-)
--
0: {'¥>-
2. S : (+> (- = -1(-}
LJ. (-) -­
,· (+)(+- ....
.
lo·
(.+)
a-
)(+ ��
(::� -2..)v ( � 5)
42.
Word Problems
The perimeter of a rectangle is 46 feet. Express its area A as
a function of the
width of a si e.
J._
�
1,A.J
Qw
11
)t-
43.
·
.:
-z,vJ
A ::. J_ . �
= z.3-w) w
- i- f/\)
A-ex:) =- zol.,U - w
�ft �zj_
��[-..
A projectile is lauriched upward from the ground. It's heigh
t, s, in feet above
the ground is given by the equation s = 64t - 16t2 • After how
many seconds in
the air will it hit the ground?
b b 2...
[t-=--,L J se...f144.
p = .2 + 2'-/� = tJ-t-Z w
1
0 :. {:, t..J b -/
0 ;:. -/hi z_ � L/
==- -/bb (t - L./)
o
An open box is to be constructed from a rectangular piece of sheet metal
whose length is twice its width by removing a square of side 1 foot from each
corner and turning up the edges. If the box is to hold 4 cubic feet, what should
be the dimensions of the sheet metal?
: yI/ !1 , w
l
Jl).)
f I
I
I
fil!l!fw-2...
t w -2-
v ��- w. �
4 = (z().)-2-)(w -z....) (,)
LJ =- 1,l)J _ '-/w - 2 w -I- '-I
-------2-_fo
W
0
-L-
.=.. 2-W
0 =--2-w
(w-?J)
{)) :::.- 8�+
,l -==- � -1 .LL-+"