•
§]
Name
__
WORKSHEET
Date
_
Period
- POLYNOMIAL
__
§]
Sketch the graph of each polynomial (no y-scale) using the roots of the
function.
y..__ - \
FUNCTIONS
16. f(xl = 5x(x - 113
17. f(xl = (x + 1)(x - 21(x + 41
y.. ~ ?- ..,'"
'1--;'-
Determine if each of the following is a polynomial function. If yes, give the
degree and number of terms. If no, explain why not.
\W....
-;2.
1. f(xl = 3x~ - 2x + 4
~ ..
~f>4~e~r-€eJ
4. f(xl = 9x3 -
J2 x2 S,3a:t~<u)
'f-
7. f(xl =
ili
d6t~..e
f(xl = 40
3. f(xl = 4,( - 2~
Vf'i-¥(f(1
(I D
5. f(xl = 3x3(X2- 21
5x + 6
'4'*~
~ 5'~:t~((r'.-)
5x
8. f(xl =
x+1
(is)
9. f(xl = (x
_~_10.
~~
y
t
x3 - 4X~ 25x + 100)
(y...1-_75)(_ 'Y..
23. f(xl = x5
-
512 + 4x
). ('tt'5~\q..)
-'+J (_)£.k*-S)
~"l.._4) (t.~-,)
~ 1-'0(..~t;)~tI)
')
B
A
2-)
12. f(xl = x' - 4~
---
'(.?-('r'/b.v.)..IJ>'"
r:\"
13. f(Xl=-x3+4'(~4X
)
-X(')('1--4~+4
( '1. -"l..\t~--z.)
14. f(xl = -x· + 4x2
__
-
,........._ 1---
-i--- .
-
I-
--r-
-
I-
i
:r+............,-+-+-+-+-r-ol
t
i----
r
- t.. f'
- ~
~
-1--- f-
i---
- r-r-
. __
15.f('j~l--)T~~t[i
-=1 _
,-t 1
It~\ -:~
I-
v....
I-
c--
x
x
I
~I--
f- i---
-~(_
'/.
(~,&'J.j.~")
C
I 1 ;~
f(xl
(x',)
~('t~~~&~,_
.f\
-~ , .
18.
","_Cj.. -4)-~~(f..-4)
-\-I.f\
C'J.~')-)(jk%-)
11. f(xl = x3 - 4,( + 4x
---
c
2
31
f(xl = x + 4~ + 4x
i)
~
r
3\e~
Ma1ch the polynomial function with its graph.
3
D
"tl ~~deJ(e~
nD
()D
()
x
x
f-l
6. f(xl = 2 -
--I-
t_
~--.
f-~
T":"
0-
l+l r .
=~~if
-r-
l-
f\-~~(
'f-._
r-
\]I
Determine algebraically if each of the following functions is even, odd, or
neither.
26. f(xl=-x5+18x3-81x
-z...
27. f(xl=-x~+4'(
~t'j.)~-(-'l.)H~(-~~<6l(:-~ ~h)::-(-"..)'\
'1&;)
, :::: ",5 _ \~ ~\ %\)(
__ ~ '-l -\ 4~
r
'5
- \ ly--); 'A --
oclJ.
~
(6 'J. r~\~
~
£~~'(\
e
Name
WORKSHEET
(\
I A 14-2 I
__
Date
_
Perlod
- WRITING POLYNOMIAL
_
FUNCTIONS
1. I am a cubic with roots at -2, -3, and 1. (2, 40) is a point on me. Write my function in
factored form and sketch me.
y
i{~):: G\. (
'j.. -{ ~ )(
7. f(x) has a minimum of -4 at x = 2. Write in polynomla,-I_fo_rm_.
_----,~--~
f ('I- j=d.X{).. (1-....3')
'1-. t ~
)('k - ,')
~) l'_)::,
~ ('2-):: a ( L\-') ( ej)( \) -::SQ.o.... -;; ~
0..--::' ~
1>
ZU
.
L\) (-\')
(;;t) == -~~~*
'A \~
tt>')::: -'-f~( '(.-J.)('f.. + f)
~
-~'1.(~1._)(-;t)
?
~'y~ -~~
,).
~
~
f'(6)
-:oL3~ '6)
z:
x
\'C'1-") ;;; a~31L\-)(r
4. I'm a quartic with a double root at -1 and a double root at 2. (1,5) is a point on me.
Write my function in factored form and sketch me.
tit'
~ (~)-.;().(y..1r \ j (1--;;-;"
-r (-\)- ta.:; S
/1>,5
lA.- ...;;.--
11
+('f)~ ~ (j''r\)(",,~t
(5) ( -.;1.-)&3)
o._.:; -~
::t10
o..~;;J._
.f(~) -;.~ 'J.?U,t;).-)
~'(_\y: ()._L-;;.
'i")
~ I ga_::: -3\0
y
'-t~
(~t'~)( X- 3)tk
(A ( \ )
m a e;UOIe; wnn a OOUOIe root alO and a root al·2 that goes through (3, 90). Write my
function in polynomial form and sketch me.
(X t-;l.)
I
8. Goes through (1. -36). Write in factored form.
+(\)::
~
I
~()Cr~.1.
Q,:::-
~~ (y.):"X
+4'£ +-~)l
Ltc{ ~ .~~
r
2j(_~) ~ X Cx/3)
2. I'm a cubic with a point at (1,8) and roots at 2. -1. and O. VYrite my function in
polynomial form and sketch me.
y
(A_
0.. [1-)2( ....,):: -
x
\£(~') ::~('" *~)('/..t~).:j. -lJ)
~ C~)=o:x('I. -~J('i.H)
ret)::
[A14!]
.~
I"
x
-Pc~); -JX(~.f'~)(_'j..-3)(y.4)-
I A 14-3 I
I A 14-3 I
Name
_
WORKSHEET
Date.
_
Period
Given that g(x) is a factor of f(x), completely factor f(x). Then answer the
questions about the function f(x).
;---.
__
- LONG DIVISION OF POLYNOMIALS
5. f(x)=x3-7x+6,g(x)=x-2
X').·t
Rewrite f(x) using the Division Property. If the remainder is zero, completely
factor f(x).
1. fix) = 3x2 -17x -15. g(x) = x - 4
2. fix) = 3x3 + 2X2-19x + 6. g(x) = x2:!" x - 6
).-
x-tte~~~~I~~
) 3~- II3~-5
'j.
'X~-x.,-(P)3~t~~~\q
-I '5"
--35
X
~
~')(.1-:1)(.
G~ [email protected]_)(.
il""
5.
t
~
..Jt
'l~:
~ Jl-/.. ~i-?>
"3
•
2b
-)(
x~t_D;X
"
1
tOle
?,-/) ftc t).)
~
1 1(". 46><'- 80b
.?p,g.
'l<. -t "C>
~ )\-~
t3><-
o
[o x a. -.;:? Xl'fs
:t~
e\o,,"'Fo
rf-.----__:::?
()_qt
'" - 6, Q('"
"f.-,'3 ('I..-t i) t ("/...
~i)
('AJr. d-) L'f-?~\)
~\' J.-) ()<. \' \) l",Z-k ~ -'\ \)
f(')~
(A
{
tl)(&tS)(-dJ<.B))
r
between
(ld
3, - 2
(
3·
\(rJ
b
- '1'bll"'B))L
q't.-b
- <1 ')(
,Wh,",
c) What
r"
j.~ 0
• 0'
'3'
.
3;
't ) Lj
domain of ftx)?
tne
..
is f(O)?
(.- 0::>0 I?OJ
('
-\-
(.0) ~ - (p
\ l.t'l.- \ 10 HS' Wh." ',1("
('1>( - \ )L'ft.- 3)
1-)'
-1;. .".0
;.(:1- -1
,'1--0('+'1
X ~ 1- J_ 3
~~~O/t"I;-'"
-'fh'~3~1
(;,
'l~'~>1\1
what two
= 6? 'f,.'?_ 1'I- f ~:;.
&
is fix)
c) Where
~"_I>-J.J
1.)\O,_ I~ t.,
wnere " f("
?-
I
zeros?
.....
_ .? 1< \- 3
]\~:;)
b) f(x) has a minimum
x=-0\,
C?~~
\.'J!I",)S -i'fJ,-IJ.2\1-tl)lttJl."t
x
X t;A ~ -3
('J... \-'.3) (J..-- \ )
:2."'''tD)<tl)~'t\D''
<9
yE>!(
i" f1# \
_
;:;J:!'~VI
t- 'X_- ~
•.f(". 6><'. lOb, •
~ 'tPX' L1 3
v. _.t ;;!
6, Q("
(f) ~~')("_ ,1- nt'-t-DX-"'\
X _d,
y
?-
~+3)()l.-;L)L
3.
f(x) with no y-scale.
~
C~·+-?J()'--~)
" _. "j,,-,-2
f(,"" _.><,.,.,
_
QkLf)(o'i-5)
-@
~~~II 3
a) Graph
@)< -d..y.~
'X t-~
~/~ffi:/~t
& s~'-f~O
-1'h - 2>
("f.-;;t)(2St3J[')(_-1 /
X-~) ~o>fr7y.t-/t?
,
(:9,3/~f3y-~@\~>,
-5~15'
f(x) =
,
O?
•
14 \~l H:)oo)
/",~'I
< ";;1
j.'
[/"14-3
8, f(x)
= x'
- 6x3 + 5x2 + 24x - 36, g(x)
= x2 -
4 f(x)
=(y... t ;)_
)(y..- ;l) l ')(- 3)( 'I.- 3)
~
2.
X tD)I_- 4)
~
'1-.- (Px +9
}._:-~~
\5/ tJ..Lf)( -310
fbx-;~-t
~~,/;
G>~
('l-t;)')(Y-.-;))(
;}) -;z ) 3
b) At x
t-~'1- ~ {.:\4 ')(
~fA.~3 ~~
a) Find the intercepts,
= 3, f(x) is increasing,
or neither.
decreasing,
~/\.
<f.;l.~)l
~}t
X -3')ly._-?:>')
c) Where is f(x) < O? (
-;;J_.
)
)
f}-
d) At x = -2. f(x) is increasing. decreasing,
or neither.
'-}1J.iJ:AeA
I