direct or inverse variation. Write the equation that models the relationship.

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1 Name. Block Date Version A Algebra 2: Chapter 8 Test Review 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 y < What type of variation relationship exists? Circle one: Direct or ^Inverse) Write the equation that models the data in the table: _ y Plr/V. i r. t ST" What type of variation relationship exists? Circle one: Direct or Inverse Write the equation that models the data in the table: _ Suppose that x and y vary inversely. What is the constant of vajiaiiojijtx= 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/m2) 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. If 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 100th. 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^. /? J s * A. Find k, the constant of pro B. Write the equation that C. What is the value of = 24 and z = 6? 7 The amount of oil used b 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,

2 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 ) - J its JC - 2x-3 JC 2-9 /jt(v*y) wit Vertical Asymptote -= r 3 Horizontal Asymptote Vf I (^T~> End Behavior ~» gg fc^ > JC2 +3JC + 1 4JC 2-9 Vertical Asymptote "a J Va. Horizontal Asymptote y«'/v End Behavior x"-> go <^-=>H *.x-3 (* + l) 2 Vertical Asymptote 'Horizontal Asymptote End Behavior -=? - <7*».2+7JC + 12 x + 4 -^/Vertical Asymptote \! ' H o r i z o n t a l Asymptote A)«N»a- End Behavior -» - Pfx") 9 Write the equation of the graph shown below. It is a transformation of y = , *.. J_... -» )...! - La L t::q.. :.JLJ Graph the function. Be sure to include all asymptotes on the graph. Identify the vertical asymptote, horizontal asymptote, domain and range. Vertical Asymptote: 3 y i^j-ocf 1 jt Ti 1111 i~frr H Wo W y. 4 Horizontal Asymptote: )/- O Domain: AlI rril> e/c^f ^ Range: All r^l»yf<-jflf y / ^ 11 What describes the end behavior of / (x) = 3JC 2x + \ as x approaches ±oo? - y - ' ^ k 12 Identify the vertical and horizontal asymptotes of the function: f (x) x = 0 y = 1 x = 3 y = 0 x-4 No Vertical Asymptote No Horizontal _ ^ Asymptote Y~ *

3 "3 ) Name. Block Date --^ J^_^\/ej2U0ri 13 Graph: 6x + l 3x-2 -ft- 1 il i V T h ft \ «1» (1 "7 i 1" -i ^6 7 TO" I/.7 J" the var 14 5x2y loxy4 ly 3 ~ 6x + l 2x x + 2 2x (+O 15 4d2+Sd 2d Jt 2+9x + 18 JC * + 3* + 2 i- 1"* x + 2 3* + l 19 4x 2-4*+l 8JC^4_^ 2 Q 2x2 + 5JC - 3 2x3-8x 2 - J

4 Name JC + 4 Block mi} Directions: Solve each rational eaua tion. Check vour solution V»- 41 The steps options given. Steps Justification 8/ / Given Expression /-15/ (-6-20)+ (8/-15/) (-6-20) + (8-15)i -26-7/ Substitution Property Associative Property V of Addition/ Closure Property of Addition \^Co7n m utative^n. Property of Addition UT- jr r from the (Distributive ^Rrppertyy Identity Property of Addition Inverse Property of Addition 42 Identify the property: If 2/-4 = x+3,and x+3 = y, then 2i-4 = y "fremi.\yc ) f 'TJ If I" ^yjp-' o^o^r^ 43 Solve the quadratic equation for its roots: 3JC(3JC+2) = 3.*-4 /a

5 Name Block Date Version A 44 Find the inverse of the function: /(x) = 8.x3 46 >i 3,/ Y± - v I Which fu horizontal asymptote as y =?.t -1 y= r^>0 y = <$x~y / I > ^ x2^ c ^ _ +A 8 y = 46 Indicate the intervals where the graph of f{x)=2^ x + 20 is only increasing throughout the interval. <fr<~ 47 Identify the end behavior as x approaches +co of each graph below: 1 i-w TO B R - fi I] f 7? y ->. y -> fe CT y -> <=»Q

6 Name Block Date -Veisiun A" l^^ldentify the domain and range of/0) = -(2jt2-4)+2. Does the function g(x) same domain and range? - 2y * + f + ~L = -2 JC+5 +6 have the Graph both f(x) and g(x) on the coordinate plane: ft*, -t«vs Pc, o 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 ^/ - j / -/o t- zo - /6 M/?x -/ox AO 1* * r V JT 3 V) -ijt- - d -

7 96) [l^x f >2,? v"* ^ 3 ax5-2? - o 2_ -ft *

8 ^x z - 2. x-) 1 x 2ycl fr-t - ^ c# K - S c?

9 ~7 Zi) l -fx a. 5 "2- Hx "7,fx/ 2xy' L t- 3>. c^xyvy 3-Yx "^& -r *-\~L i 3 x - i ; u V3^x"'^ 3 x"- I 2. ru~* " 3 -^ J f -T" CP ' 3 ^\<5 '

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