~NSName Date Class _

Graphing Cubic FunctionsPractice and Problem Solving: AlB

)( 'j'X~;l, :3 -,;;..

,--,

--:-1 -s---Z -.;<,-3 ,

-lJi I

(-;;. -).. (-I,y)

j::- (t(x- h»)3-rIL

_?;)Y+ I

-0)3+- I

i , yIi G,

i I I . .I !

1 if ~{xj : !'I I (3 , ).<

, i I! I !! Gi i (2. , ) (3;-1tX1~ ;;( K

, ! iO . I I ---~ 1=-4 I -+--li i I I II -+--1i j TL

I< •

I 141

! ,I- I I

I 1 I I I I .

QC )( 1::. C;).,( >c--'.»)'j IJ

2. g(x = -3(x + 2)3 - 2y

+1 y , i < iI i 114 ! l

,:

I i I i~

I

I (,1 3) ( ,21 - I

q.ll :-1I ixj

1=4 l 0 L i I~I 1 I

~ --t-iI ! I! ! J

! I I TlI I 1 j i

__ q()J,: ~'!?-f~

Solve. -"f '3 + ( I5. The graph of f(x) = x3 is reflected across the x-axis. The graph is then

translated 11 units up and 7 units to the left. Wiiiethe equation of thetransformed function."____ 1L\CJ:

Write the equation of the cubic function whose graph is shown.

3. 4.

Calculate the reference points for each transformation of the parentfunction f(x) = x'. Then graph the transformation. (The graph of theparent function is shown.)

<

1. g(X)=(X-3)" +2

y

-Li 1 1 iiI'Til! !TTTTl

t IXi

6. The graph of f(x) = x3 is stretched vertically by a factor of 6. The graphis then translated 9 units to the right and 3 units down. Write theequation of the transformed func}ion. 3

~ Lol)c-~) -jOriginal conlen! Copyright@b oughton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

75

Name Date Class _

Graphing Cubic FunctionsPractice and Problem Solving: C

Calculate the reference points for each transformation of the parentfunction fIx) = x'. Then graph the transformation. (The graph of theparent function is shown.)

1 g(X)=-~(X-3)' +2. 2 2H++-+-OD;j-. -.-.-;-:UJ:~.":£J~~l~'::'=-'TlJ-f~ 1 i , ! I ! i :_:; ,'!' 1. 3. . . . :: .. j ... .L 1..., ; --4'-'1.1.. .. 1I: ~ .T-'

;<

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)-' 1'36. 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 finalgraph. 3_jjK)-=O - (x+lj~-~5 _

Original content Copyright@byHoughton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor,

76

Graphing Polynomial FunctionsPractice and Problem Solving: AlB

N~me Date Class _

liiiIdentify whether the function graphed has an odd or even degree anda positive or negative leading coefficient. ~ pa>

1. ! i i! ii,!! 2.!! i i ! I!! 3...--t'-'i"-"i~"".j""._._..~~~_..~ ~ !...... . :1 ~.. _ .. ,I i.~_~_:~~ :_.~ ; _~.:..l = ... , ,; ;,;; -+ -~~'Mj""~'1.. -.- _' .-. - - _' --. --.

:::::~r~:I=:r:=:::":.~~:~:r~::r:::I:::~r~:::' _ ;~ j l"'J'-~" •••••••-i.~ ;_ J ~...... : : r--.f ..v.i j .•• "! •••. ~.; ••. ' .•• r T .

Use a graphing calculator to determine the number of turning pointsana the number and type (global or local) of any maximum orminimum values.

•. y .i , i : , ,,

I :, ,, , ; ,

i : ,,

Below x-axis:

Above x-axis:

5. f(x)=-x'(x-2)(x+1) 3-hum~ po"t')I-IDW tYlaK I CJlo~ fYlO)(. I 10co..1

)

7. f(x)=(x+2)(x-3)(x-1)

o L/'t:.. IX,>i

Below x axis:

6. f(x)=-(X-1)'(X+3)

f.;-H ...

4. f(x)=x(x-4)'

~~ynl ~ ~<J/ n;1sI OCaJ!.. t\t ) I 1 oc i0i1tA1 .

Graph the function. State the end behavior, x-intercepts, and intervalswhere the function is above or below the x-axis .•

Original content Copyright@byHoughton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

80

Name Date Class _

Graphing Polynomial FunctionsPractice and Problem Solving: C

"

" i ~.~.ni.; ~ ..._.J L L,,,j .

i ';

Identify whether the function graphed has an odd or even degree anda positive or negative leading coefficient.

1. , , 2........, '--++" "ii

....... "-1 "'i'~'"

\11;'I

Use a graphing calculator to determine the number of turning P9intsand the number and type (global or local) of any maximum orminimum values.

)(-y 0.- ) -rbe.) "'7 - oPx' :7-00 +: (~) -7 -..,..p

(-.;<,6) (" 0) ~(3j 0)

(I ) '-1)X '- I t1l'C/ )( ) 3

! I i ii

I , \i ! ,I !I U,

\"i 1\

i , 'JV ,i1\ I, I 'k

I +End behavior:

x-intercepts:

Below x-axis:

Above x-axis:

5. f(X)=X'(X-3)(X+2L, I ID(~

~ +u-~"l~ PPlko..l 1l'W¥/'",

i i

Below x axis:

,.:"'_J....

: ;+1'_ ~ -FC"')-7-rc()

't,~ 'r'\ •End behavior: X -"2""""I t{ It}':; ooD

(-310) (-~IO) (O{,D)Above x-axis: x< -;, 'irX")-;)"" ')

)

(-3) ,-;<)

x-intercepts:

4. f(x)=-(X-1)'(X+2)

I +u. ((11 ~ Pt-'/ C)lo bed

Graph the function. State the end behavior, x-\!)tercepts, and intervals 'where the function is above or below the x-axis. ; V .> ,.. _ ~

6. f(x)=(X-2)'(x+2)(.>:+3) 7. f(x)=-(X-1)'(X+2)'(X-3)- X ,\( ,x:. X

i i :_:~.;l\-~I-~ X-;;I..,i x~ -", , - ~,..;/ .

X";. '3

Original content Copyright@by Houghton Mifflin HarCOurt. Additions and changes to the original content are the responsibility of the instructor.

81