Name. Block Date Version A

Algebra 2: C h a p t e r 8 T e s t R e v i e w

Directions #1&2: Determine if a variation relationship exists. Describe the data in the table as a direct or inverse variation. Write the equation that models the relationship.

X 1 2 5 10

y 0.25 0.125 0.05 0.025 <

What type of variation relationship exists? Circle one:

Write the equation that models the data in the table: _

Direct or ^ I n v e r s e )

X 1 2 5 10

y 0.25 0.5 1.25 2.5 Plr/V . i r . t ST"

What type of variation relationship exists? Circle one:

Write the equation that models the data in the table: _

or Direct Inverse

Suppose that x and y vary inversely. What is the constant of v a j i a i i o j i j t x = 12 when y = 4 ?

Sound intensity is inversely proportional to the square of the distance from the source. Suppose the sound intensity is 30 watts per square meter (W/m 2 ) at 8 meters. What is the sound intensity at 4 meters? ~J~ •= \c ^ _ _ ^ i _ /a^v -"yT^ l^to

The maximum load a cylindrical column can support varies directly as the fourth power of the diameter and inversely as the square of the height. A column that is 2 ft. in diameter and 10 ft. high can support up to 6 tons. I f a column is 1 ft. in diameter and 12 ft. high, what is the maximum load it can support? Round your answer to the nearest 100 t h .

Suppose that y varies jointly with w and x and inversely with z and y = 175 when w = 5, x=20, and z = 4. y = k ^ X . / ? J s *

A. Find k, the constant of pro

B. Write the equation that

C. What is the value of

7 The amount of oil used b

= 24 and z = 6?

Ip traveling at a uniform speed varies jointly with the distance and the square of the speed. The ship uses 34 barrels of oil in traveling 60 miles at 20 mi/h. How many barrels of oil are used when the ship travels 32 miles at 23 mi/h? Round your answer to the nearest tenth of a barrel, if necessary. ^ - iQ<i c-2, *-/

A 3.0 barrels B 45.0 barrels C 18.1 barrels D 24.0 barrels,

Name Block. Date. Version A

Directions: Write the equations of the asymptotes for each function in the blank provided.

8 Find all vertical and horizontal asymptote(s) of each function. As x approaches positive infinity, what is the end behavior of each function?

/ tsss X / j T ( V * Y ) wit

) - J

JC - 2 x - 3

J C 2 - 9

. x - 3

(* + l ) 2

Vertical Asymptote X-= r 3 Horizontal Asymptote V f I

( T~> End Behavior X~» g g fc^ — >

JC2 +3 J C + 1

4 J C 2 - 9

Vertical Asymptote 'Horizontal Asymptote

its

. X 2 +7 J C + 12

x + 4

Vertical Asymptote X" a J Va. Horizontal Asymptote y« '/V End Behavior x"-> — go

< -=>H * -^/Vertical Asymptote \! ' H o r i z o n t a l Asymptote A)«N»a-

End Behavior X -=? - <7*»

End Behavior X - » - ° ° Pfx")

9 Write the equation of the graph shown below. I t is a transformation of y =

-3 -

- 8-. ... .. ,7.. ... - * .. J_ . . .

- » 1

).... ! - • La L t::q — .. :.JLJ.

X-+

10 Graph the function. Be sure to include all asymptotes on the graph. Identify the vertical asymptote, horizontal asymptote, domain and range.

111111111-Ti 1111 i~frr X H W 3 y i^J-ocf 1 •

j t - 6

Vertical Asymptote:

y. 4

Wo X

Horizontal Asymptote: )/- O

Domain: AlI r r i l > e /c^f X^ £

Range: A l l r ^ L »yf<-jflf y / ^

11 What describes the end behavior of / ( x ) = 3JC

2x + \

12 Identify the vertical and horizontal asymptotes of the function: f (x)

x-4 No Vertical Asymptote

No Horizontal _ ^ Asymptote Y~ •—• *

x = 0

y = 1

x = 3

y = 0

- — y - ' ^ k as x approaches ±oo?

Name. Block Date -- __J _ \/ej2U0ri

13 Graph: 6x + l 3x-2

-ft- 1

il i |

X V T

h

1 » —

ft - 1 - 1

1

\

1 «

1 1 (1

"7 i

1" - i

^6

14

15

16

5x2y lOxy4

4d2+Sd 2d

J t 2 + 9 x + 18

JC + 6

l y 3 ~ 6x + l 2x - 5 22 +

x + 2 2x + 4

7 TO"

I/.7 J" the var

23 8 9

• + -

17 * + 3 * + 2 i - 1 " *

3* + l

2 (X+O

x + 2

19 4 x 2 - 4 * + l 8 J C^4_^

2 Q 2x 2 + 5JC - 3 2x 3 - 8 x 2

- J

"3 )

Name Block

1 + 31

JC + 4 mi}

Directions: Solve each rational eaua tion. Check vour solution.

4 3 X -V»-0

41 The steps options given.

UT- j r r

from the

Steps Justification

8/-6-20-15/ Given Expression

- 6 - 2 0 + 8/-15/

( -6-20)+ (8/-15/)

(-6 -20) + (8 -15)i

-26-7/ Substitution Property

Associative Property V of Addition/

(Distr ibut ive ^ R r p p e r t y y

Closure Property of Addition

Identity Property of Addition

\^Co7n m utative^N. Property of Addition

Inverse Property of Addition

4 2 Identify the property: If 2/-4 = x+3,and x+3 = y, then 2i-4 = y "fremi.\yC o^o^r^ y ) f ' T J I f I " ^yjp-'

43 Solve the quadratic equation for its roots: 3JC(3JC+2) = 3.*-4

/ a

Name Block Date Version A

44 Find the inverse of the function: /(x) = 8.x3 46 •>i 3,/

Y± - v I . 3

4 5 Which fu horizontal asymptote a s y = ? .t - 1

y= r^>0

y = <$x~y / I > ^ 1

5 + 3x2^

c ^ _ 8 +A

y =

46 Indicate the intervals where the graph of f{x)=2^- 3X 2 - 12x + 20 is only increasing throughout the interval.

<fr<~

1 i-W X TO

4 7 Identify the end behavior as x approaches +co of each graph below:

B 7 „ 4—

9 • R - fi -1 • 4 | - I]

f 7 ?

235

y ->. y -> fe C T ° y -> — <=»Q

Name Block Date -Veisiun A"

l^^ldentify the domain and range o f / 0 ) = - ( 2 j t 2 - 4 ) + 2 . Does the function g(x) = -2|JC+5|+6 have the same domain and range? - 2y *•+ f + ~L

Graph both f(x) and g(x) on the coordinate plane:

© ft*, -t«Vs Pc, o -

-1 6

49 Rewrite the following nq expression with rational exponents: $ll7x6v*_zL.~

* y

50 Write the polynomial of least degree in expanded form with the following roots: 5, -2, and 4i

Ljjf-/o)(yVn '5

t -

^ / - j / - / o

/6 M/?x -/ox A O

z o -

1* * r V JT

3 V)

- i j T - - d -

^ 3

96) [l^x f >2,? v"*

a x 5 - 2 ? - o

2_

-ft •

*

^ x z -X X

2 . x - ) 1 x

23.

2ycl fr-T X - ^ c#

X - 0

1-K - S

c?

X

~7

5

Zi) l -fx a.

"2- X

"7 Hx

, f x / 2 x y ' L

"^&X

t-

-r-

3> X. c^xyvy

3 - Y x

X

2 *-\~L

3 x - i ; u V 3 ^ x " ' ^ 3 x"- I 2. ru~*—"°

- 6 7-

i

X

3 X - ^ J X - 12-

X

CP

' 3 \<5 '

X f -T"

X

3 X 2 x

12,Mr

3x

Z X 6 O

K