Mock Exam 3 Name~~~ __~~ _

The graph of a quadratic function is given. Determine the function's equation.

1) --v( ",IL)

P(X, d)'2.

-::I (~--'t) .•.Z.-2.

-a --~.(. z.\ ~2

d':: a(l<...k)~t~'I.

Go = q,( 0_-2.) -\- 2..••

" Z Q. 2,.. -to '2.

~ ::--L( Q "" 'Z..

&.J::.'i.,

E~i1B) g(x) = (x + 2)2 - 2

D) j(x) = (x - 2)2 - 2

v c ..z., z..)

fC c:>,b)

-4

-6

-8

.. -'10

.. \.:: .•• I~..... b

.. ··,4

A) f(x) = (x + 2)2 + 2

C) hex) = (x - 2)2 + 2

1)

y

2) _

\1C"'-J"')

(>(~ })~

d " -I- Cx ••• ) + -.3

~~_~Ly

Z

~-:.o.()(-~) +t:.7..

-t:.q (4-0) -t-3>

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..f ::Lt q ->- Lf -:: I.{ q

~1

v C o,-?')

P ( 2, ..:J-)

.\.....

.. . -

....

10

'8

6

4

2

-10 -8 -6 -4 -~2

h'-8I

. (10

2)

A) hex) = -x2 - 3

C) j(x) = -x2 + 3

B) g(x) = -x2 + 6x + 9

D) f(x) = -x2 - 6x - 9

3)

D) (8,0)

4)

D) (-7,6)5)

D) (2,40)

C) (7, -6)B) (7,6)

B) (I, 0)

Q~ 't I b::: 9 ,C :. BB) (1,20) C) (-2,16)

V(-~Jf(-I5J I-(~):: ~'(-t) z.re(-'~t'8

E(-IJP). Jot .• ) ;}

(j) M b.e..,ll "'" h > of1/'1-,/ ~ ~ VV\e.rll2J '".:.--.----- -::::.

U,..pJ~).;d d ~rV~

(CF j-_ '1)< Z t?)( r fi

!j {X 'l.-t 2..;< ).if: 7S

'-({/t-lX +/"Z. ) ;-- !!;j"'Z..

/-(?c)-=- '1 ex +,)2.-t Lf ~r-\ vC -I) 'tJ

- --- ---- -

7) __

D) [-I,:c)C) (-x, -4]B) (- x, -1]

7) f(x) = (x + 1)2 - 4

A) [-,4, x)

/II.-l,: TTtIL a..,t;•• ",f So".•...(tva i••tie. x- e."f.·"•..t •f t{ Ve.vot¥-MAC 1105 - College Algebra V (6. J ~ JFind the axis of symmetry of the parabola defined by the given .9uadratic function. t-- q..(. ,'j, uft,

6) f(x) = l1(x - 3)2 + 5 V (~)~) ~'~ et,'f- :. ~ >, ....'0 ~0) x = 3+ B) x = 11 'f"4 1) x = -3 D) x = 5

ind the range of the quadratic function. (2.A ""e c....'1, 4t1)

Use the vertex~ intercepts to sketch the graph of the quadratic function.

V(-I(I() 8) Y + 3 = (x + 6)2 0 -= (X +6)? - 3>

\J( -CoI·~)

x

B)

x

I8)- .L..l ...z,-0

-~_S

,.l---If

l

C) D)

x x

2

MAC 1105 - College Algebra

9) f(x) = - 2x - 3 + x2

A)

c;-= l 10-:''''

2....,.f Or) -:: X -2. X -1>

x

B)

o

~.~

, .•

Z -~

3 0

9) __

~("I)t{~Jl(l)+(z)

fC-~)

C)

x

D)

x

x

Determine whether the function is a polYEomial functiont. w~t FF C,l(OoAe."" J1O)f(x)=4x+4x5 • r~ql R:- CDt..rffIC,t't..t.ts

A) Yes • 1;lI\"of.p~cl~t Vc."l·ca~) No

- 2. Jj _ )J 0 "'~ 4 t,..,c. ~ 'I~ t:f11) i(x) = 4 - ~ = L{ - X - f/

W B)Ye,

10) --11) _

MAC 1105 - College Algebra . ~Find the degree of the polynomial function. ZP

12) f(x) = 4x - x2 + ~ -:::> - X r'f X.,.. ~A)2 B)1 C)4 D) -1

12) __

Determine whether the graph shown is the graph of a polynomial function.

13) ,A if:Y , CD!' h'llvc:>J S {J ~ocrfK bLl

lviii. q~ C(b(~pt >~,It tff.

-tJe.. vui~ @ (0,0)x

13) __

A) not a polynomial function

14)

A) polynomial function

x

B) not a polynomial function

14)

B) origin symmetry C) neither

15) --

16) __

· St.,.., ~ ~/-/ ~I\J

rf-( ~~) -=- I- (kJ

~: X ~~---rckJ~

({ ~) ==C:z..) ::: /

.[ (t..) ~ z.. 2--;. y/-(-t..) ~{("LJ /t

~~ l..;.".j·;OA> t4Ve

>(J •••.•.•~ (-r'L Q I>•• -t~ (/-r..y:IJ (abu,e)

({ -~) -:..-fCic}

~: trte) -:-}(3

f{-3) = [-3J '3 = _l 7

If 3) ;:. :;' -:.. 11­

Ir -f) --- I (It)

~(-~);:;- f (~)-1..=1 -:.-zt /

MAC 1105 - College Algebra17) 17)

A) origin symmetry B) y-axis symmetry C) neither

Divide using synthetic division.18) (5x5 +13x4 + -2x3 + x2 - x + 97) -;-(x + 3)

A) 5x4 - 2x3 + 4x2- llx + 32 + _1_x+3

B) 5x4 - 2x3 + 4x2 - 11x _ 33 + _1_x+3

18) __

5C) 5x4 - 2x3 + 4x2 - 12x + 33 + -­

x+3

5D) 5x4 - 2x3 + 4x2 - 12x - 33 + -­x+3

Use synthetic division and the Remainder Theorem to find the indicated function value.

19) f(x) = x5 + 8x4 + 2x3 - 6; f( -4)A) 890 B) -890 C) 50 D) 1914

19) __

20) _

C) f- 2. -4 2}L 3' ,B) f2., 4, 2}P

Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solvethe polynomial equation.

20) 3x3 - 13x2 - 6x + 40 = 0; 2

A) f- 2. 4 2}L 3"

5

1D) ± 2' ± 1, ± 2, ± 4

~~:I:'~/"! ..,~:r"Z..,>1-'2... ~ ..:!:'l...I:t(

Use the Rational Zero Theorem to list all possible rational zeros for the given function.

21) f(x) = -2x3 + 3x2 - 4x + 81

A) ± 2' ± 1, ± 2, ± 4, ± 8

111C) ±-, ±-,±-,± 1,± 2,± 4, ± 8842

F dIn the domain of the rational function.

22) h(x) = 8x2(x + 4)(x + 5)

A) lxlx;;t -4, X;;t -5f

C) {xlx;;t-4,x;;t-5,x;;t-8}

i!l!t: fJ' ~) f> i:D lIX+L.i~O I X+.s~~tXj-'t] Ig;- sJ

(}) (5? t-13x <.( -2. 'X ~ '/-X 2._X t '77).!:- {x+ ~

XT~~ 0 --:JX- ii~ 5 l~ -2- I -[ t.}.

~ -17 to -(L ~,J -ib

~./ '1 -I/:; 5-b - ZZ L./~

\ ~ ~/~ Sb -z~~

.. ./ ({ -'tJ -:- ~'Iv )

N ~~~~ f4. xl.I X

fop/Nt> wUf:' Ptl.s.s/d

t ~~lart>A i;) ~U&>S

-~o-;1/ 1

23)

x -;..-.3

4 6 8 10 x-10 -8 -

MAC 1105 - College AlgebraUse t!le graph of the rational function shown to complete the statement.

23) I

"ft' 1 ~,p("c)a4~~ 1-4_ ~ ~~ \o)f loOoV Ie -6

--.... -8~ -10

As x-+-3- f( )I X ---""?

A) -x . B) + oc C)o D) 3

2

24) __

10 x

-4

-6

-8

-10

-10 -8 -6 -4 -2-2

10+Y

8

6

4

24)

,I A> ~ i:199t.ac1IS

t d:;) I'

As x-++ "', f(x)-- ?

A)O B) +x C) -x D)1

Find the vertical asymptotes, if any, of the graph of the rational function. )x ( .\ _ )C (v_ (,)(XfC, \:'0

25) g(x) = ~ ~ ~J -G _~\-(X..u" 1\ ~ 25)

x2 - 36 'I. 'OJ I~ . -:..6@ 6, x = -6 B) x = 6, x = -6, x = 0 -= -6C) x = 6 D) no vertical asymptote 1\

Use transformations of f(x) = .!.or f(x) = l:..- to graph the rational function.x x2

6

MAC 1105 - College Algebra

26) h(x) = x: 4 ~

10

8

6

26) __

-6

/(~)-;,F__/7 t:

-

cj]"A)B)

10 y

loly

8

8

6

6

4

4

2

2

-10 -8

-6-4-2 26810 x -10 -8-6-2I2468lOx-2

-2

-4

-4

-6

-6

-8

-8

-10

-10

C)

D)

10

y10i y

8

8

6

6

4

4

2

2

( I

IIIt-10 -8

-6-4-2 246810 x -10 -8-6-4-2I24/'6 810 x-2

-4-6

-8l

-8-10

-10

27)

6

B)

6iy4

2I

IIIII-6

-4-2

-2-4-6D) 6iy4

~I

I

IIII-6

-4-2 246 x

2 4 6 x

2 4 6 x

2

-2

4

-6 -4 -2

-6 -4 -2

C)

-2

-4

-6 ---------------~4,_-~~+(

B) x = -9, x = -5

D) x = - 36

Find the vertical asymptotes, if any, of the graph of the rational function.

28) x - 36x2 - 14x + 45

A) x = 9, x = 5

C) x = 9, x = 5, x = - 36

28)

8

Ib-X

~

t(~)'- _x + / b _ X ~x --xt

ref') ::- X + XG ~ X ~~A f. ~ ) ~ :x

:: x ...•~}(

~e: ~~~

x+-b=O

rx :=:-b I

6iJ 3>)< \/ ~x-h .c... D2-

:!x +lBX~-Z -17, £.0

3X(X+b) -:()(-fG) 60

0+ b'J( 3>X-1) !::- 6?J)(-I ~ ()

?,J( ==- I

0"- ~7

F

( +)

2-

x= -10 -:> ~ ("'u) of J ~ (-Iu) -6 = l2.lJ~o Fx ~ 0 -) 3' 02 f-I ~. 0 -b := - b .!: 0 Tx";. , -i> 3' I Z i- 11. 1 - ~ ;::. ('1 ~ 0 F

-x+~x-~ 2. 0

) - Xt S c; ();<= g

T

-Ool-r -2x=o-? ~=->o0-> 3..-

X'/b ~ ~K •• 3:- >0- ~ ­6-~

'ir- (f) ~ -lot'8 -Z'\_ ·7 __ ;. - Z b10 -.> 1-

MAC 1105 - College Algebra

32) x + 12 < 3x+9 32) __

( IIIIIIII111II)-12-10 -8 -6 -4 -2 0 2 4 6 8 10 12

15A) (-::c, -9) or (- 2'::C)

( I I) I( I I I I I I I I I I )

-12 -1 -8 -6 -4 -2 0 2 4 6 8 10 12

C) (- oc, - ~5) or (9, oc)

( 1 I ~ I I I I I

I I I (I I )-12-10 - -6 -4 -2 0 2

4 6 8 10 12

15B) (-9, - 2)

(

I I fj I I I I I III1I)-12 -10 - -6 -4 -2 0 2 4

68 10 12

D)0 (

IIIIIIIIIIIII)-12-10-8 -6 -4 -2 0 2 4 6 81012

x+ 12.. L .3XM

~

-r ...,~, ~ ,-

T- "'t"S"

~

-,-IO+'~ ~

X::. - (V -.)

.c:.J -? - ~ >-IDr1 -/

-1. ~ ~

-rlLu ~

)(=-8~

- ~.•.Il.}i~j-~~ -)- S,.., I

L... J.s

- zX L.. 1..$--- --l -~

X > w 7-,5

_______ )( -=- 0

li-~J -"!) .11. (_1-.> I ~

x+ Il(X+4)'- L ~(~1'1)

7\ .,...,

~ ~X-l- L~

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10