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Name _______________________________________ Date __________________ Class __________________ MODULE 8 Rational Functions Module Quiz: B For 1–2, build a rational model, f(x) for each situation. Then solve the model for the given value of x. 4. Does each set of data represent an inverse variation? A 1. Sara and her friends are going on a day trip to the fair. The total cost for taking the train is $178.75, and the cost of each fair ticket is $15. How much does the trip cost per person if 5 people go? B _______________________________________ C 2. A social studies class is taking a field trip to the history museum. The cost for renting a bus is $250, and the entry fee for the museum is $8.75 per person. To the nearest cent what is the cost per person if 21 people go? D 3. Choose True or False for each statement (2 x 3) . about the function f ( x ) (2 x 7) B f (x) True 0.75 3 7.5 x 1.5 3 5 y 5 2.5 1.5 x 10 20 25 y 0.1 0.5 4 x 0.3 0.4 0.6 y 10 7.5 5 True Yes No Yes No Yes No Yes No False False C The graph has a horizontal asymptote at y 1.5. False 7 . 3 True False D The graph has a vertical asymptote at x 3.5. False 7 D f(x) has a vertical asymptote at . 2 True y B The graph has a vertical asymptote at x 1.5. False C f(x) has a vertical asymptote at 5 True 1 9 (3 x 7) True 2 A The graph has a horizontal asymptote at y 3.5. 1 4 (2 x 7) True 0.5 5. Choose True or False for each statement about the graph of the rational function 3x 4 f (x) . 2x 7 _______________________________________ A f (x) x True False 6. Membership in a fitness club costs $45 per month plus a one-time registration fee of $102. Write a rational function for the average monthly cost of an x-month membership in the club. Then find the average monthly cost of membership if a member leaves after 6 months. False ________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 43 Name _______________________________________ Date __________________ Class __________________ MODULE 8 Rational Functions Module Quiz: B 7. Identify the horizontal and vertical asymptotes of the function 1 f (x) 3. Then graph the 3x 6 function. 11. Find the domain and range. ________________________________________ 12. Describe the end behavior. ________________________________________ 13. Sketch the graph of the function. _______________________________________ 8. Write the function graphed below in the a form f ( x ) k. xh 14. Li Ming rowed 2 miles upstream and then 3 miles downstream. His average speed rowing in still water is 2 miles per hour. The model that describes the situation is 2 3 s 10 f (s ) 2 s 2 s (2 s )(2 s ) where s is the average speed of the current and f(s) is the total amount of time that Li Ming rowed. Sketch a graph of the function and use it to determine the average speed of the current if Li Ming rowed for 3 hours. _______________________________________ For 9–13, use the rational function x 2 x 12 f (x) 2 . x 3x 4 9. Find the vertical asymptote(s). _______________________________________ 10. Find the point(s) of discontinuity. ________________________________________ _______________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 44 Name _______________________________________ Date __________________ Class __________________ 13. 14. A 15. f ( x ) x 3 39x 70 16. f ( x ) x 3 5x 2 9x 45 17. f ( x ) x 4 9x 2 112 18. 4i, 1, 1 19. 3, 3i 1 20. , 1, 2 3 14. MODULE 8 Rational Functions Module 8 Quiz B 1. f ( x ) 178.75 15; $50.75 x 250 8.75; $20.65 x 3. A True B False C False D True 2. f ( x ) 4. A No B Yes C No D Yes 1 mi/hr 5. A False B False C True D True Module 8 Quiz Modified 102 6. f ( x ) 45; $62 x 7. y 3, x 2; 1. C 2. B 3. f ( x ) 33 7 x 4. $18 5. Domain (, 3), (3, ); Range (, 2), (2, ) 6. B 7. A 8. y 1, x 2; 8. f ( x ) 4 3 x 2 9. x 1 7 10. 4, 5 11. domain x | x 4,1, range 7 y | y 1, 5 12. as x , f ( x ) 1 , as x , f (x) 1 9. B 10. $16 Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 45