,::<

I •

OassID _ N~e _ Date _ SCore _

Practice Set 1 Parabola parts dlmgutierrez

"..I'

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Give the focus, directrix, and axis for the parabola. A)&e> ~Ird ~t P)'IMD'ro-\ CbCls I eq.Vll{"tilOV1.1) x2 = 16y Ve"b'tes . etc. 1) _

A) (0,4), Y= -4, y-axis B) (4,0), x = 4, x-axisC) (4,0), Y= 4, y-axis D) (0, -4), x = -4, x-axis

.'

12) _--x2 = Y 2) :.40

{A) (-20,0), x = 10, x-ct*is B) (0, -10), y = 10, y-axis

,I

C) (0, 10), Y= -10, y-axis D) (0, -10), y= 10, x-axis't~"r;-:",;:--

3) x =9y2 3),,.~l.

A)f~'o} x =- ;6' x-axis Bl6'l= ~,x-axj,:7'."

'J,:

C) !,o}x=- !,x-axis D) 0, 316' Y= - ;6' y-axis"~\.;

~.;t-:','

,~

~'. 4) y2 = -12x 4)1~

f· A) (3, 0), x = -3, x-axis B) (-3,0), x = 3, x-axis.q;~~ C) (0, -3), y= 3, y-axis D) (-3,0), Y= 3, y-axis..~.~1.('

5) (x + 2)2 = -28(y - 5) 5)f~'.

"A) (-2, -2), y= 12, x =5 B) (-2, -2), y = 12, x = -2

.: C) (-2, -2), y = 12, x = 6 D) (-9,-2), Y= 12, x = -2:~:.;-",.:" 6) (y - 5)2 = -4(x + 4) 6)1;~~~.,,:!~l.• A) (-5,4), x = -3, Y= 5 B) (-5,5), x = -3, Y= -4:~

C) (-5,5), x = -4, Y= 5 D) (-5,5), x = -3, Y= 5r;;'

"~,~

7) (y - 2)2 = 20(x - 3) 7)A) (7,3), x = -3, Y= 3 B) (2, -2), x = -8, Y= -2C) (8,2), x = -2, Y= 2 D) (-2,2), x = 8, Y= 2

8) (x + 4)2 = 4(y - 2) 8)A) (2, -3), y= -5, x = 2 B) (4, -1), v= -3, x = 4C) (-4,1), x = 3, Y= 2 D) (-4,3), Y= 1, x = -4

1

Practice Set 2 Parabola equations dlmgutierrez

OassID _ Name _ Date _ SCore _

"MULTIPLECHOICE. Choose the one alternative that best completes the statement or answers the question.

Write an equation for the parabola with vertex at the origin.1) Focus (5, 0)

A) y2 = 5x B) y2 = 20x C) x2 = 20y

2) Focus (0,9)A) y2 =9x B) y2 = 36x

3) Through (-7,7), opening to the left

A) y2 = -7x ~ B) x = .ly2~' 7

C) x = -7y2

4} Through (7,6), opening to the right36 36A) y2 = - -x B) x = _y27 7

2 49C) x =-y6

5) Through (-J7, 7), opening upward

A) y = 7x2 B) y = x2 C) x = -J7 y27

6) Through (5, -10), opening downward'2 _ 5

A) x = - _y2 B) x2 - - -y5 2

7) Through (6, -6~), symmetric with respect to the x-axis

A) x = 36y2 B) x = ~y2 C) y2 = 36x

8) Through (6,6), symmetric with respect to the y-axis

A) x2 = 6y B) Y = 6x2 C) x= -6y2

Write an equation for the parabola.9) vertex (4,10), focus (4, 12)

A) 2(y - 10) = (x - 4)2

C) Y - 10 = 8(x - 4)2

B) (y - 10)2 = 8(x - 4)

D) 8(y - 10) = (x - 4)2

10) vertex (7, -9), focus (10, -9)

A) (x - 7)2 = 12(y + 9) B) x - 7 = 3(y + 9)2

D) l(x - 7) = (y + 9)24

C) (y + 9)2 = 12(x - 7)

1

1)

D) x2 = 5y

2)

D) x2 = 36y

3)

D) x2 = 7y

4)36D) y2=-x7

5)

D) x = y2

6)

D) Y =lx25

7)D) x2 =--J6y

8)D) y2 = 6x

I··.. , .,. ,'.

I..I·...". '

i1

, .I .I

i·

r,',

I'.

I'

I::::'(:',I::':"I.",I'

1'-:, .t ..I"I

9) _

I.

10) __

~.., .

I .." .

11) vertex (-3,4), focus (-14,4)A) x + 3 = -44(y- 4)2q -44(x - 3) =: (y + 4)2

12) vertex (-5, -9), focus (-5, -13)A) (x - 5)2 =: -52(y - 9)q 16(y - 5) =: (x - 9)2

13) vertex: (-4,4), directrix: y = 11A) (x + 4)2 =: -28(y - 4)q (x + 4)2 =: -28(y + 4)

14) vertex: (2, -4), directrix: x = 10A) (y - 2)2 =: -32(x + <U::tq x2 =: -32(y - 2)",'

II,

11) I!B) x + 4 = -14(y - 3)2 j

.'D) (y - 4)2 = -44(x +3) I

f(

li

12) I•• •• ~.

B) (x + 5)2 =: -16(y + 9) !D) 16(y - 9) =: (x - 5)2 IIII

13) I

lB) (y + 4)1 =: 8(x - 4) I!

D) (y + 4)2 = -28(x - 4)

14)B) (x + 4)2 =: -32(y - 2)D) (y + 4)2 =: -32(x - 2)

tII(r·r!I

I'

iI

Ii

!IjI,I

iII

!

2

Pfc]'cti~ Set .3 Ellipse and graphs

'. 'dassID ---- Name _ Date, _ SCore _

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Graph the ellipse.x2 v2

1)-+"'- =136 4

,!,1) _

x

y

A) B)

10 10

5 '

y y

-10 -5 5 10 x -10 10 x

-5

-10 -10

C) D)y y

50 50

-50 50 x -50 50 x

-50

1

'.x2 v2

2)-+"'- '=116 25

2) _

y

A)

C)

-10

x

B)

50

, y

10

5

-50 10 x50 x -10

-50 -5

-10

D)

-5

x-50 505 10 x

-10

2

"3) 4x2 + 64y2 = 256

-10 5

y

10

5

10 x-5

-5

-10

A} B}y y

I':.~.

10 10

5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10 -10

C} D)y y

10 10

5

-10 10 x -10 10 x

-5

-10 -10

3

3} _--:-_

· ' 4) 49x2 + 9y2 = 441-.

10

x

y

5

-10 -5

A) B)~' y y

10 10

5

-10 10 x -10 -5 5 10 x

-5

-10 -10

C)

-10

105

-5

-10

D)

10 10

yy

-5 105 10 x -10 -5 5

-10 -10

4

x

4)

'. 5) (x + 1)2 + (y + 3)2 = i4 9

10

x

y

5

105-10 -5

-5

-10

A) ~ B)y y

10 10

5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

C) D)y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5 -5

-10 -10

5

5) _

.,'"

6) (x + 1)2 (y - 1)2 = 116 + 9

5

5 10 x

y10

••

-10 -5

-5

-10

A) B)y

10

5

-10 5 10 x -10 -5 5 10 x

-5 -5

-10 -10

C) 0)y y

10 10

5 5

-10 -5 -510 x -10

-5

-10 -10

6

10 x

6) _

Practice Set 4 Ellipse parts

OassID _

dlmgutierrez

Name _ Date _ SCore _

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question .••

Write an equation for the ellipse.1) center at origin; length of major axis 10; y-intercepts ±4

x2 v2 x2 v2 x2 v2A) - + ...£.- = 1 B) - + ...£.- = 1 C) - + ...£.- = 15 4 16 25 4 5

2) foci at (-2,6), (-2,0); major axis length of 10(y - 3)2 (x - 2)2 1

A) 25 + 16

C) (y - 3)2 + (x + 2)2 =t25 16',

(x - 3)2 (y - 2)2 _B) 16 + 25 - 1

(x - 3)2 (y - 2)2 _D) 25 + 16 - 1

3) minor axis from (-5, -4) to (-1, -4); major axis from (-3, -8) to (-3,0)(x - 2)2 + (y - 4)2 _ (x - 3)2 (y - 4)2 _

A) 4 16 - 1 B) 4 + 16 - 1

C) (x + 4)2 (y + 3)2 = 1 D) (x + 3)2 (y + 4)2 = 14 + 16 4 + 16

4) eccentricity ~; foci at (3, 0), (-3,0)

x2 v2 x2 v2A) -- + ..I.- = 1 B)-- + ..I.- = 1

9 16 16 9

5) foci at (0, 9), (0, -9), through the POin{I' 41~J

~+L-A) 1600 1681 - 1

x2 LC) 1681 + 1600 = 1

x2 v2C)-+..I.-=116 25

x2 v2B) - +..1.-= 1

40 41x2 ..E.-

D) 41 + 40 -1

1

x2 v2D) -+...£.-= 125 16

x2 v2D) - +..1.-= 1

25 16

1) _

2) _

3) _

4) _

5) _

c.: ','" .....,>

I' '':I',

r ....r •>

1 " •

I": "

I'r

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I·':~.[i..:,.I.'

i ., .

(,' .r:~.. '. .I, :

to· .

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. "!,I.I'"

Class ID _ Name _ Date _ Score _

'.;

., '

\ • I ,r:: -Practice Set) Hyperbola and graphs

.',.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Graph the hyperbola.i!:.. x2

1) 25 -'4= 1 1) !':"'.

I'

5

If'

y

10

-10 -5 5 '" 10 x

If: .i.'

-5

-10

A) B) ' ..r.·

10t:

I·I.',r!.II,',

l",t

r

y

-10 -5 5 10 x

C) D)

10 10

y y

5

-10 -10

,.

I',

1

",

x2 v22) --...1..-= 19 36

'.' 10

y

"5

'.5 10 lC-10 -5

-5

-10

A)'~'.

B)

-10 ro x -10 10 x

<:;",:'" ..:':'1~\~":,~.~~ C) D)..

y y,.. 10 10

, .~.'~:..~. ,~ .

'15

t::,.: ':

x -10 -5 5 10 x

-10 -10

2

2)

-10 -s S 10 l(

-5

-10

A) ~. B),,'.

"y y10

,~."

"I

3).:I,Il ,

\'"f.

I,t,;

I"I

Li.l:rIrII

I,I,r.fI

3) (x - 3)2 _ (y + 2)2 = 125 36

10y

-10 10 x -10

-10

C) D)

5

"t

~

I

I

I;' I~ -10 -5 5 10 x

~;:~ -51.

i'-10

"

~:"

3

4) (y + 3)2 _ (x - 2)2 125 49

10

10 l(

y

5

·10 ·5

·10

A)

·5

B)

10

y

·10 ·5 10 x

·5

·10

C) D)

y10

5 5

·10 ·5 5 10 x ·10 ·5 5 10 x

·5

·10

4

4) _

ri ', '

II( "

I',:.

I':r:~:.::,':

':', '

','

•.5) 4y2 - 25x2 = 100

5

5) _

y10

••

·10 ·5 5 10 x

·5 I

.'

.10.'.-::

A) B) I ' .

y <r~ y10 " 10

"

5 5.'.

·10 ·5

·5 ·5

·10 ·10

C) D)",:.......

·10 ·5 10 .X ·10 10 x

""','

'.' .

5

.':.:

"-t,.-10

C) D)y

10

..

-,,:.,';

"

"!~..1...·.. ;

',":

,f~.

,.1

4.

It.,';

6)

I,

I:" I:

I,1',

6) 16x2 - 4y2 = 64

10

10 x

y

5-10 -5

-5

-10

A) B)y

10

-10 10 x x

-10

-10 10 x -10 -5 10 x

-5

6

Practice Set 6 Hyperbola parts dlmgutierrez

OassID _ Nmme _ Oate _ Score _

. :,,'

"MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the center, foci, and asymptotes of the hyperbola .x2 r..

1)9- 16 = 1 1) _

4A) C: (0, 0); F: (0, -4), (0, 4); A: y = IX, Y = - x

3 3B) C: (0,0); F: (0, -4), (0,4); A: y = "4x, y = -"4x

~ 4 4C) C: (0,0); F: (-5,0,,:-<5,0);A: y = IX, Y = -"3x

3 30) C: (0,0); F: (-5, 0), (5,0); A: Y = "4X, Y = -"4x

r.. ~-2) 36 - 64 - 1

4 4A) C: (0, 0); F: (-8, 0), (8, 0); A: Y = IX, Y = - IX

- 3 3B) C: (0,0); F: (0,-10), (0, 10);A: y = "4x, y = -"4x

3 3C) C: (0,0); F: (0, -8), (0,8); A: y = "4x, y = -"4x

4 4D) C: (0,0); F: (-10, 0), (10,0); A: Y ="3x, Y = -"3x

2) _

3) (x + 3)2 _ (y + 3)2 = 19 16

3 3 3 21A) C: (-3, -3); F: (-3, -8), (-3, 2); A: y = 4x - "4' Y= - "4x + T

4 4B) C: (-3, -3); F: (-8, -3), (2; -3); A: y ="3x + 1, y = -"3x - 7

16 7 16 7C) C: (-3, -3); F: (-7, -3), (1, -3); A: y = TX +"3'y = - TX +"3

16 1 16 7D) C: (-3, -3); F: (-3, -7), (-3, 1); A: Y = TX -"3' y = - TX +"3

3) _

........

1

(y - 4)2 (x + 1)2 _ 14) 400 - 225 -

16 8 16 8A) C: (-1, 4); F: (-11,4), (19,4); A: Y = 9x - 45' Y = - T"- 45

4 16 4 8B) C: (-1, 4); F: (4, -21), (4, 29); A: Y=3"x -3'Y= - 3"x-3"

4 16 4 8q C: (-1, 4); F: (-1, 29), (-1, -21); A: Y=3"x +3' Y = - 3"x +3"

16 16 16 8D) C: (-1, 4); F: (4, -11), (4, 19); A: Y = 9x - 45' Y = - 9x - 45

4) _

5) x2 - y2 = 8 .'I"tA) C: (2, 2); F: (4, 0), Ct-\ 0); A: Y = 2x, Y = - 2xB) C: (0,0); F: (4,0), (..:..'4,0);A: Y = x, Y = - x .q C: (0,0); F: (4,0), (-4, 0); A: Y =2x, Y = - 2xD) C: (0,0); F: (2,0), (-2,0); A: Y = x, Y = - x

5) _

2

OassID _ Nmne _ Date _ Score _

Practice Set 7 Hyperbola equations dlrngutierrez

..MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Write an equation for the hyperbola.1) vertices at (2, 0), (-2, 0); foci at (6, 0), (-6, 0)

x2 i!:... x2 i!:...A) 36 - 4 = 1 B)4-36 = 1

x2 v2C)--..L-=l

32 4x2 v2D) __ ..L-= 14 32

1) _

2) vertices at (3, -5) and (9, -5), passing through the point (-6,9)(x - 6)2 (y + 5)2 (x - 6)2 (y + 5)2 1

A) 9 - 196 ~l= 1 B) 9 - 331- -15 ~ 15

2) _

(x - 6)2 (y + 5)2 _C) 331 - 9 - 1

15

(x-6)2 (y+5)2D) 196 - 9 = 1

15

3) vertices at (0, ±4), asymptotes at y = ± ~ x 3) _

v2 x2A) -L- __ = 1144 16

.E ~-B) 16 - 36 -1

.E_ x2 _C) 16 144 - 1

v2 x2D) ..L- __ = 136 4

4) vertices (-4, -5), (-4,9); eccentricity ~

(y +4)2 (x - 2)2 = 1A) 9 - 49

(y - 4)2 (x + 2)2 = 1C) 49 - 9

4) _

(y - 4)2 (x - 2)2 = 1B) 49 - 9

(y - 2)2 (x + 4)2 = 1D) 49 - 9

:'

5) center at (6, -13); focus at (6 - yJiO, -13); eccentridty ~.

5),',

•. A) (x + 6)2 _ (y -13)2=1 B) (x - 6)2 _ (y + 13)2 =1. 81 9 9 .81"

C) (x +6)2 _ (y -13)2 =1 (x - 6)2 (y + 13)2=19 81 D) 81 - 9

1

·.Practice Set 11 Limits algebraic functions

Class ID _ Name _

dlmgutierrez

Date _

•..

Score _

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the limit, if it exists.

1) lim x2 - 2x - 15x--5 x + 3

A) -8

x3 + 12x2 - 5x2) lim

x--O 5x

A)5

3) lim x2 + 2x - 80x -- 8 x2 - 64

A)O

4) hmx4 -1--

x--l x-I

A)2

5) Hm2

h--O ,J3h+4 + 2

A) 1/2

6) lim 7x + h

h-» 0 x3(x - h)

A)~x4

7) !im(x + h)3 - x3

h--O h

A) 3x2 + 3xh + h2

8) lim ~-1

x--O x

A) Does not exist

9) lim(l+h)1/3- 1

h--O h

A) 1/3

B) Does not exist

"." " B) Does not exist

B) 2..8

B) 4

B) Does not exist

B) Does not exist

B) a

B) 1/2

B) 3

C)5

C) -1

1C)--8

C) Does not exist

C)2

C) 7x

C) Does not exist

C) 1/4

C)O

1

D)O

D)O

D) Does not exist

,D)O

D)1

D) 3x2

D)O

D) Does not exist

1)

2)

3)

4) ,'.

5) _ . "....

6) _

7) _

8) _

9)

j, ."

One-sided limits: special pc-wise defined functionsPractice Set 12 dlmgutierrez

Class ID _ Name _ Date _ Score _

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.A

Use the graph of the greatest integer function y = lxJ to find the limit.

1) lim lxJx-2- x

1) _

2) lim lxJx-2+ x

3) Iim [3x 1'r\x-0.5- "

"

4) lim [3x]x-O.5+

5) lim lx/3 ]x-0.5+

6) lim [x/3 ]x-0.5-

Find the limit.;]

7) lim lzl:4 x--'O+ x

J8) Jim

lz.lx-O- x

9) lim h=1lx--.2+ x-2

10) Jim ~x-2- x-2

11) lim ~x-2+ 2-x

12) lim ~x-2- 2-x

13) lim CX-3{J::~lJx-+-1-

2) _

3) _

4) _

5) _

6) _

7) _

8) _

9) _

10) _

11) _

12) _

13) _

r. -:, 1._....r·',:f<I.'.·,

i,l',l' ,

I'

i.:

i'I,rI,

, "

,-"

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r" ,, ,

1

,'<',',

r'"

,f ',

j".

f' ,

r',"f

Practice Set 13 One-sided limits: concepts dlmgutierrez

Class ID _ Namc _ Oate _ Score _

"MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.1) Given lim f(x) = LI, lirn f(x) = Lr, and Ll '" Lr, which of the following statements is true?

x-+O- x-+O+1)

1. lim f(x) = L)X-+O

II. lim f(x) = Lrx~O

III. lim f(x) does q.~t exist.x~O .'.'

A) III B) none C)IJ 0)1

2) If lim f(x) = L, which of the following expressions are true?x~O

2)

1. lim f(x) does not exist.x~O-

II. lim f(x) does not exist.x-+O+

III. lim f(x) = Lx~O-

IV. lim f(x) = Lx~O+

A) III and IV only B) I and IV only C) I and II only D) II and III only

3) If lim f(x) = 1 and f(x) is an odd function, which of the following statements are true?x~O-

3) _

1. lim f(x) = 1x~O

II. lim f(x)=-1x~O+

III. lim f(x) does not exist.x~O

A) II and III only B) I and III only C) I and II only D) 1, II, and III

4) If lim f(x) = 1, lim f(x) = -I, and f(x) is an even function, which of the following statements are 4)x-+l- x~l+

true?I. lim f(x) = -1

x~-I-

II. lim f(x) = -]x~-l+

III. lim f(x) does not exist.x~-l

A) I, II, and III B) I and III only C) I and II only D) II and III only

1

Class ID _ Nrume _ Date _ Score _

"..Practice Set 14 Infinite limits dlmgutierrez

..MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question .

..'.

.~'.

Find the limit. Write the equation of the vertical asymptote/s, if any.

1) Hm 11)

x~-2+ x+2 \'A)-oo B) -1 C) 0 D) 00

2) 4 2)hm 2x --->--3- x - 9 'rt

A) -00 B) 00 C)O D) -1

3) lim x23)---

x --->-0+ 2 x

A) 00 B)-oo C) Does not exist D)O

4) limx2 - 5x + 4

4)x3 - xx --->-1-

A)-oo B) 0 3 D) 00C)--2

I.I

x2 - 3x + 2II,

5) limx3 - x

5)I.x--->-O

-I

A)2 B) 00 C) Does not exist D)-oo I1!

6) lim [_1_ - 1 J 6)x __ 5- x4/5 (x - 5)4/5

A)-oo B) a C)OO D) Does not exist

':'".

:',

I"II

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1

.' .'r::t;' Practice Set 15 Limits at infinity dlmgutierrez"" i',,''"" Class ID Name Date Score

t:1-., I, r·,,~ ..:f.: I

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ,,:~I

~: Find the limit. Use the indicated limit to identify the equation of the horizontal and oblique asymptote/s, if any.',':!' x2 + 8x + 6" Jim 1)1)

x~oo x3 - 9x2 + 5.:"-,'

B)i"

A)O C)1 0)001t.'5

2) Urn -9x2 - 8x + 2 '1'\ 2)-3x2 + 3x + 16x~-oo "

A) 3 B)1.. C)1 D) 008

3) Jim 5x3 + 3x23)

x - 6x2x~ - 00

::'; B)-oo 1 0)00~,

A)5 C)--2

~{ r-,

,.~~:

1.••·1 4) lim --2 4)/ x~oo x~'.-;

A) -1 B) -2 C)2 0) -3I

"I

5) lim -5 + (2/x) 5)5 - (l/x2)X~-oo

A)-oo B) - 1 C)OO 0)1

6) lim 26)

x~-oo 4 - (7/x2)

A)-oo 2 C)1..B) -- 0)23 2

7) Jim 49x27)

2 + 4x2X---700A) 49 B) 49 C)~ 0) does not exist2 4 2

8) lim-3"Jx + x-I

8)3x + 3x~oo

A) -1 B) 00 C)O 0)13

1

·,"1 j .I ,

39) lirn '$-5x + 7

9)X--oo -7x + x2/3 + 2 ,~

B)~q~ .. !A)O 0)-00 :

7 5

10) lirn (4x - --j16x2 - 5x + 6) 10)X-oo

A)O 8) -12 qi 0)-008

11) lirn --jx2 + 12x - x '1'-\. 11)x-co ~~~,

"A)6 B) 00 qo D) 12

12) lirn (--j3x2 + 7 - --j3x2 - 3) 12)x-co

A)O B) 00 q 1 0)-j32~

13) lirn ~x2+2_x-~x2_7x 13)x-co

5B) 9 q~ D) does not existA) -- 2 2

I'i

2