Name: Class: Date: a. yes; 32 c. yes; 10 b. yes; 0.25 d. not an inverse variation
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1 Name: Class: Date: Algebra II Decide whether the data show inverse variation. If so, find the missing value. a. yes; 32 c. yes; 10 b. yes; 0.25 d. not an inverse variation 2. It takes a train 8 hours to travel from Capital City to Johnson City when it travels at a speed of 65 mi/h. How long would it take the train to go the same distance when it travels 40 mi/h? 13 a. 13 h c. 8 h b. 11 h d h 3. The price per person of renting a bus varies inversely with the number of people renting the bus. It costs $15 per person if 44 people rent the bus. About how much will it cost per person if 71 people rent the bus? a. $9.30 b. $24.20 c. $ d. $ The wattage rating W (in watts) of an appliance varies jointly with the square of the current I (in amperes) and the resistance R (in ohms). If the wattage is 6 watts when the current is 0.2 ampere and the resistance is 150 ohms, find the wattage when the current is 0.3 ampere and the resistance is 300 ohms. a. 180 watts c. 27,000 watts b. 90 watts d. 27 watts The variables x and y vary inversely. Use the given values to write an equation relating x and y. 5. y = 3 5, x = Decide whether the data show inverse variation. If so, find the missing value. Determine whether the equation shows direct variation with the square. 7. b 37 = a 2 8. It takes a train 5 hours to travel from Capital City to Johnson City when it travels at a speed of 72 mi/h. How long would it take the train to go the same distance when it travels 45 mi/h? 1
2 Name: 9. Which function matches the graph? a. f(x) = x 1 x 5 b. f(x) = x 4 x 5 c. f(x) = x 5 x 4 d. f(x) = x 5 x Which is the graph of f( x) = x 2 x 1? a. c. b. d. Sketch the graph of the function. Include any vertical or horizontal asymptotes. 11. f x ( ) = 3x + 2 x + 2 2
3 Name: 12. You are selling T-shirts for a fundraiser. The cost of making the designs and buying blank T-shirts is $425. In addition to these one time charges, the cost of printing each T-shirt is $1.75. Let x represent the number of T-shirts that are printed. Write a model that represents the average cost per T-shirt. Then graph the model. 13. A new computer game costs $90,000 to develop. Once completed, individual games can be produced for $0.60 each. The first 100 are given away as samples. Write and graph a function C(x) for the average cost of each game that is sold. How many games must be sold for the average cost to be less than $1? (Hint: when graphing, use large values on your x-axis) 14. f( x) = Identify the vertical asymptote(s) of the graph of the function. 4x + 7 x 2 + 6x + 8 a. x = 4, x = 2, x = 1 c. x = 4, x = 1 b. none d. x = 4, x = f( x) = 3x 7 x 2 2x 15 3
4 Name: Graph the function. 16. f( x) = 2x 2 + 6x 2 x 2 + 2x 3 a. c. b. d. 4
5 Name: f( x) = x g( x) = Describe the function's end behavior using infinity notation. 3x 2 7x 2 + 7x + 7 a. g( x) 1as x ± c. g( x) 3 as x ± 7 b. g( x) 0 as x ± d. g( x) 0 as x 5
6 Name: 19. An accident has introduced organic waste into a pond. The decomposition process includes oxidation, where oxygen in the water is combined with the decomposing material. The amount of oxygen in the pond after t weeks can be modeled by the function O 2 = t2 t + 4 t Let O 2 = 1 represent the initial oxygen level in the pond. Which is the graph of this model? a. c. b. d. none of these Find the vertical asymptote(s) of the graph of the function and describe the end behavior of using infinity notation. 20. k( x) = x 3 2x 2 x 6 6
7 Algebra II Answer Section 1. ANS: D PTS: 1 DIF: Level B REF: MAL21159 KEY: inverse variation BLM: Comprehension 2. ANS: A PTS: 1 DIF: Level A REF: MAL21156 KEY: inverse variation word 3. ANS: A PTS: 1 DIF: Level B REF: MAL21154 KEY: inverse variation word 4. ANS: D PTS: 1 DIF: Level B REF: MAL21164 KEY: word joint variation 5. ANS: y = 21 10x or xy = PTS: 1 DIF: Level B REF: MAL21152 STA: MI.MIGLC.MTH A2.9.1 KEY: inverse variation equation BLM: Comprehension 6. ANS: not an inverse variation PTS: 1 DIF: Level B REF: MAL21158 KEY: inverse variation BLM: Comprehension 7. ANS: Yes PTS: 1 DIF: Level A REF: MAL21168 BLM: Knowledge 8. ANS: 8 h KEY: direct variation identify PTS: 1 DIF: Level B REF: MAL21155 KEY: word inverse variation 9. ANS: A PTS: 1 DIF: Level B REF: MAL21173 TOP: Lesson 8.2 Graph Simple Rational Functions KEY: graph rational function BLM: Analysis 10. ANS: D PTS: 1 DIF: Level B REF: MAL21177 STA: MI.MIGLC.MTH A2.9.1 MI.MIGLC.MTH A2.9.2 TOP: Lesson 8.2 Graph Simple Rational Functions KEY: graph rational function BLM: Comprehension 1
8 11. ANS: PTS: 1 DIF: Level B REF: MAL21176 NAT: NCTM 9-12.ALG.1.c STA: MI.MIGLC.MTH A2.9.1 MI.MIGLC.MTH A2.9.2 TOP: Lesson 8.2 Graph Simple Rational Functions KEY: rational functions graph BLM: Knowledge 12. ANS: 1.75x A = x PTS: 1 DIF: Level B REF: MAL21180 TOP: Lesson 8.2 Graph Simple Rational Functions KEY: word function graph rational 2
9 13. ANS: C( x) = 0.6x ; 225,000 games x 100 PTS: 1 DIF: Level B REF: MAL21181 NAT: NCTM 9-12.ALG.1.c NCTM 9-12.ALG.2.c STA: MI.MIGLC.MTH A2.9.1 MI.MIGLC.MTH A2.9.2 MI.MIGLC.MTH A3.1.1 MI.MIGLC.MTH A3.1.2 TOP: Lesson 8.2 Graph Simple Rational Functions KEY: graph equation word rational function BLM: Application 14. ANS: D PTS: 1 DIF: Level A REF: MAL21187 NAT: NCTM 9-12.ALG.1.c STA: MI.MIGLC.MTH A2.9.2 TOP: Lesson 8.3 Graph General Rational Functions KEY: asymptotes graph rational function BLM: Knowledge 15. ANS: x = 3, x = 5 PTS: 1 DIF: Level A REF: MAL21186 NAT: NCTM 9-12.ALG.1.c STA: MI.MIGLC.MTH A2.9.2 TOP: Lesson 8.3 Graph General Rational Functions KEY: asymptotes graph rational function BLM: Knowledge 16. ANS: A PM: Adjusted graphs per your PTS: 1 DIF: Level B REF: MAL21188 NAT: NCTM 9-12.ALG.1.c STA: MI.MIGLC.MTH A2.9.1 MI.MIGLC.MTH A2.9.2 TOP: Lesson 8.3 Graph General Rational Functions KEY: asymptotes rational function graph BLM: Comprehension 3
10 17. ANS: PTS: 1 DIF: Level B REF: MAL21184 STA: MI.MIGLC.MTH A2.9.1 MI.MIGLC.MTH A2.9.2 TOP: Lesson 8.3 Graph General Rational Functions KEY: graph rational function BLM: Comprehension 18. ANS: C PTS: 1 DIF: Level A REF: MAL21193 NAT: NCTM 9-12.ALG.1.c TOP: Lesson 8.3 Graph General Rational Functions KEY: rational function graph end behavior BLM: Knowledge 19. ANS: B PTS: 1 DIF: Level B REF: MAL21198 NAT: NCTM 9-12.GEO.4.e NCTM 9-12.REP.2 NCTM 9-12.PRS.3 TOP: Lesson 8.3 Graph General Rational Functions KEY: graph rational function word 20. ANS: x = 3 2, x = 2; k ( x ) as x and k( x) + as x + PTS: 1 DIF: Level B REF: MAL21194 NAT: NCTM 9-12.ALG.1.c STA: MI.MIGLC.MTH A2.9.2 TOP: Lesson 8.3 Graph General Rational Functions KEY: end behavior asymptotes rational function graph BLM: Analysis 4
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