Name
Date
~NS
Class
_
Graphing Cubic Functions
Practice and Problem Solving: AlB
Calculate the reference points for each transformation of the parent
function f(x) = x'. Then graph the transformation. (The graph of the
parent function
is shown.)
<
1. g(X)=(X-3)"
'j'
)(
X~;l,
:3,--, -,;;..
--:-1
-s-
2. g(x = -3(x + 2)3 - 2
+2
y
y
-L 1 1 iiI
'Til! !
TTTTl
--Z
i
-3
IXi
t
-.;<,
,
-lJ
i
I
(-;;. -).. (-I,y)
3.
i
I
i
I
3)
(,1
I
I
I
(
I
0
~ 1=4 l
I
,
+1 y
114
1
!
i
l :
q.ll
:-1
I
1
__ q()J,:
i
j
:
!'
!
I
I
i
i
,
<
,
~ 1=-4
I
!
i
I
i
j
TIL
i
I
G
if ~{x_?;)Y+ I
Ii
I I
1
(3
(2.
,
iO
I
i
,
)
.
i I
).
!!
(3;-1tX1~
I
I
I
I
I
<
•
-+--l
. .
G;;( K -0)3+- I
---
-+--1
1
!
I-4
1,
I
1
I
I I I
I
I
.
QC )( 1::. C;).,( >c--'.»)'j I
-"f
=x
y
!
~'!
?-f~
3
,
I
! J
Tl
j
Solve.
5. The graph of f(x)
,
i xj
!
I
i
I
I
~ i I
L
--t-i
I
!
I I
4.
i,
<
,21 - ~
I
!
i
(t (x- h»)3-rIL
j::-
Write the equation of the cubic function whose graph is shown.
'3
+ (I
J
is reflected across the x-axis. The graph is then
translated 11 units up and 7 units to the left. Wiiiethe equation of the
transformed function."
____
1L\CJ:
6. The graph of f(x) = x3 is stretched vertically by a factor of 6. The graph
is then translated 9 units to the right and 3 units down. Write the
equation of the transformed func}ion.
3
~ Lol)c-~)
Original conlen! Copyright@b
-j
oughton Mifflin Harcourt. Additions and changes to the original content are the responsibility
75
of the instructor.
Name
Date
Class
_
Graphing Cubic Functions
Practice and Problem Solving:
C
Calculate the reference points for each transformation
of the parent
function fIx) = x'. Then graph the transformation.
(The graph of the
parent function
1
.
is shown.)
g(X)=-~(X-3)'
2
+22
H++-+-OD;j-. -.-.-;-:
UJ:~.":
£I J~~l~'::'=-'Tl
J-f
~ 1
1. : 3
. . .
i
:;
: ..
I:
,
!
!
i
:_
,'!'
.
j ... .L
1...
;
~ , .T-'
--4'-'1.1.. ..
1
;<
Solve.
S. The graph of the function y = 3( x -
2)'
+ 7 is translated
2 units to the
right and then 4 units down. Write the equation of the final graph.
OJ!.>:}: Q (X -4)-' 1'3
6. The graph of the function y = (x)' + 5 is translated 2 units to the left
and then reflected across the x-axis. Write the equation of the final
graph.
3
_jjK)-=O - (x+lj~-~5
Original content Copyright@byHoughton
Mifflin Harcourt. Additions and changes to the original content are the responsibility
76
_
of the instructor,
N~me
Date
liii Graphing
Class
_
Polynomial Functions
Practice and Problem Solving: AlB
Identify whether the function graphed has an odd or even degree and
a positive or negative leading coefficient.
~
1.
! i i!
ii,!!
2.!!
..--t'-'i"-"i~"".j""._._..~~~_
..~ ~ !......
. , ,;
.
;,;;
:::::~r~:I=:r:=:::":.~
~:~:r~::r:::I:::~r~:::'
"'J'-~"
i
:1
-+
~.. _ .. ,I
3.
-~~'Mj""~'1.. -.- _' .-. - - _' --. --.
_;~
-i.~ i;_
•••••••
pa>
i
! I!!
i.~_~_:~~ :_.~ ; _~.:..l =..
J
j
l
j
~......
r--.fT ..v..
:
:
.•• "! •••. ~.; ••. ' .•• r
Use a graphing calculator to determine the number of turning points
ana the number and type (global or local) of any maximum or
minimum values.
~~ynl
I OCaJ!..
3-hum~ po"t')
5. f(x)=-x'(x-2)(x+1)
4. f(x)=x(x-4)'
I-IDW
~
~<J/
tYlaK
I
CJlo~
)
n;1s
t\t ) I 1 oc i0i1tA1 .
Graph the function. State the end behavior, x-intercepts,
where the function is above or below the x-axis .
•
6. f(x)=-(X-1)'(X+3)
and intervals
7. f(x)=(x+2)(x-3)(x-1)
•.
f.;-H ...
i
,
,
i
:
y.
,
,
I
,
i
:
,
, :, ,
;
,
,
Above x-axis:
Below x axis:
o L/'t:..
I
Below x-axis:
X,>i
Original content Copyright@byHoughton
I 10co..1
fYlO)(.
Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
80
Name
Date
Class
_
"
Graphing Polynomial Functions
Practice and Problem Solving: C
Identify whether the function graphed has an odd or even degree and
a positive or negative leading coefficient.
1.
,
......., '--++
"
,
2.
"ii
.......
"-1 "'i'~'"
\11;
'I
" i ~.~.ni.; ~ .
L,,,j .
.._.Ji L
';
Use a graphing calculator to determine the number of turning P9ints
and the number and type (global or local) of any maximum or
minimum values.
4.
f(x)=-(X-1)'(X+2)
I +u.
5.
Pt-
((11 ~
,/'"
'/ C)lo bed
I
ID(~
~ +u-~"l~ PPlko..l
1l'W¥
f(X)=X'(X-3)(X+2L,
Graph the function. State the end behavior, x-\!)tercepts,
where the function is above or below the x-axis.
6. f(x)=(X-2)'(x+2)(.>:+3)
i
i
.
!
,
I
i
I
,
i
x
axis:
X";. '3
1\"
-FC"')-7-rc()
'JV
I
I
'r'\
•
End behavior: X -"2""""I t{ It}':; ooD
Below
,
1\ I,
't,~
Above x-axis:
,
U
i
: ;+1'
x-intercepts:
x~ -", , - ~
\
.:"'_J....
_ ~
X
X-;;I..,
\
!
!
_ ~
,x:.
X ,\(
i
i
I
,
i
.> ,..
i
I
i
'
7. f(x)=-(X-1)'(X+2)'(X-3)-
:_:~.;l\-~I-~
,..;/
i
and intervals
;
V
End behavior:
(-310) (-~IO) (O{,D)
x< -;, 'irX")-;)"" ')
(-3) ,-;<)
)
x-intercepts:
,i
'k
)(-y+0.-
x'
-r be.)
)
"'7
+: (~)
:7-00
-..,..p
(-.;<,6) (" 0) ~(3j
Above x-axis:
(I ) '-1)
Below x-axis:
X '-
I
t1l'C/
Original content Copyright@by Houghton Mifflin HarCOurt. Additions and changes to the original content are the responsibility of the instructor.
81
oP
-7
-
)( )
0)
3