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Precalculus: Graphs And Models, A Right Triangle Approach, 6th Edition Test Bank

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    Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) 3( 2 x + 1) = 9 - 5( 2 x - 3) 1) A) - 9 16 B) 9 16 C) 21 16 D) 21 Answer: C Explanation: A) B) C) D) Graph the equation. 2) y = - x 2 - 4 2) A) B) 1

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    C) D) Answer: C Explanation: A) B) C) D) Solve the problem. 3) Find the average rate of change. Value of Car in Thousands of Dollars Number of Years of Use 3) A) $ 2.00 per year B) - $ 2.00 per year C) - $ 3.00 per year D) $ 3.00 per year Answer: B Explanation: A) B) C) D) Use substitution to determine whether the given ordered pair is a solution of the given equation. 4) 7 3 , 1 4 ; 6x - 4y = 13 4) A) Yes B) No Answer: A Explanation: A) B) 2

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    Solve the problem. 5) The total amount of mail delivered to 22 million Canadians in 1999 was 7.4 billion pieces. On average, how much mail did each Canadian receive in 1999? 5) A) 0.3 pieces B) 336.4 pieces C) 3363.6 pieces D) 33.6 pieces Answer: B Explanation: A) B) C) D) 6) In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.90 as soon as you get in the taxi, to which a charge of $2.00 per mile is added. Find an equation that can be used to determine the cost, C(x), of an x - mile taxi ride, and use this equation to find the cost of a 4 - mile taxi ride. 6) A) $11.08 B) $10.90 C) $10.78 D) $11.80 Answer: B Explanation: A) B) C) D) 7) Helen Weller invested $ 10,000 in an account that pays 12 % simple interest. How much additional money must be invested in an account that pays 15 % simple interest so that the average return on the two investments amounts to 13 %? 7) A) $ 7000 B) $ 5000 C) $ 10,000 D) $ 6000 Answer: B Explanation: A) B) C) D) Is the following correspondence a function? 8) 8) A) Yes B) No Answer: A Explanation: A) B) Graph the function. 3

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    9) f(x) = x 2 - 2 9) A) B) C) D) Answer: D Explanation: A) B) C) D) 4

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    Use the given graph to find the x - intercept and the zero of the function. 10) 10) A) ( - 3 , - 4 ); - 3 B) ( - 3 , 0); - 3 C) (0, 0); 0 D) ( - 4 , 0); - 4 Answer: B Explanation: A) B) C) D) Find the midpoint of the segment having the given endpoints. 11) ( 5 , 6 ) and ( - 3 , 4 ) 11) A) 4 , 1 B) ( 2 , 10 ) C) 1 , 5 D) ( 8 , 2 ) Answer: C Explanation: A) B) C) D) Use the given graph to find the x - intercept and the zero of the function. 12) 12) A) (0, 0); 0 B) ( 4 , 0); 4 C) ( 7 , 0); 7 D) ( 4 , 7 ); 4 Answer: B Explanation: A) B) C) D) 5

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    Find an equation for the circle. 13) Center at ( 2 , - 4 ), radius of length 1 2 13) A) (x - 2 ) 2 + (y + 4 ) 2 = 1 4 B) (x + 2 ) 2 + (y - 4 ) 2 = 4 C) (x - 2 ) 2 + (y - 4 ) 2 = 1 4 D) (x + 2 ) 2 - (y + 4 ) 2 = 4 Answer: A Explanation: A) B) C) D) Solve the problem. 14) 43 % of those who purchase music CDs online are 18 - 23 years old.This is three and one - half times the number who are 38 - 43 years old. What percent of online music purchasers are 38 - 43 years old? 14) A) 129 % B) 43 % C) 150.5 % D) 12.3 % Answer: D Explanation: A) B) C) D) Evaluate as requested. 15) Given that g(x) = x - 3 x + 7 , find g( - 13 .25). 15) A) 41 81 B) 1 C) 13 5 D) - 41 81 Answer: C Explanation: A) B) C) D) 6

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    Solve and write interval notation for the solution set. Then graph the solution set. 16) - 12 < - 4 x K 4 16) A) ( - 3 , 1 ] B) [ - 1 , 3 ) C) ( - 1 , 3 ) D) [ - 1 , 3 ] Answer: B Explanation: A) B) C) D) Graph the function. 17) f(x) = 1 4 x - 2 17) 7

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    A) B) C) D) Answer: A Explanation: A) B) C) D) By graphing the function, visually estimate its domain and range. 18) f(x) = x 2 - 4 18) A) Domain: ( - Q , - 2 ] 1 [ 2 , Q ); range: [0, Q ) B) Domain: [ - 2 , 2 ]; range: [0, Q ) C) Domain: ( - Q , Q ) ; range: [0, Q ) D) Domain: ( - Q , - 2 ] 1 [ 2 , Q ); range: ( - Q , Q ) Answer: A Explanation: A) B) C) D) 8

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    Solve the problem. 19) A survey of 7016 first - time vacationers showed that 80 % more vacationers took their vacation in their own country rather than travel abroad. How many vacationers in the sample took their vacation abroad? 19) A) 2506 people B) 1403 people C) 7016 people D) 39 people Answer: B Explanation: A) B) C) D) Solve the equation. 20) 3 x - ( 2 x - 1) = 2 20) A) 1 B) - 1 5 C) 1 5 D) - 1 Answer: A Explanation: A) B) C) D) Solve the problem. 21) The information in the chart below gives the salary of a person for the stated years. Model the data with a linear function using the points (1, 24,700 ) and (3, 26,800 ). Then use this function to predict the salary for the year 2003 . Year, x Salary, y 1990, 0 $23,500 1991, 1 $ 24,700 1992, 2 $25,200 1993, 3 $ 26,800 1994, 4 $27,200 21) A) $37,190 B) $37,170 C) $37,130 D) $37,150 Answer: D Explanation: A) B) C) D) 9

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    Determine whether a linear model might fit the data. 22) 22) A) Yes B) No Answer: B Explanation: A) B) Find the midpoint of the segment having the given endpoints. 23) (7, 1) and ( - 16, - 16) 23) A) ( - 9, - 15) B) (9, 15) C) - 9 2 , - 15 2 D) 23 2 , 17 2 Answer: C Explanation: A) B) C) D) Is the following correspondence a function? 24) Domain: All students attending Laughlin Community College Correspondence: Each student's Social Security Number Range: A set of Social Security Numbers 24) A) Yes B) No Answer: A Explanation: A) B) 10

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    Write equations of the horizontal and the vertical lines that pass through the given point. 25) ( 9 , - 2 ) 25) A) horizontal: y = - 2 ; vertical: x = 9 B) horizontal: y = 9 2 x + 0; vertical: 9 2 y = x + 0 C) horizontal: x = 9 ; vertical; y = - 2 D) horizontal: y = - 2 x + 0; vertical: x = 9 y + 0 Answer: A Explanation: A) B) C) D) Find the slope of the line. 26) 26) A) - 1 B) - 2 C) 1 D) 2 Answer: C Explanation: A) B) C) D) Determine the slope, if it exists, of the graph of the given linear equation. 27) y = - 1 4 x + 3 27) A) m = 3 B) m = - 3 C) m = 1 4 D) m = - 1 4 Answer: D Explanation: A) B) C) D) 11

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    Determine whether a linear model might fit the data. 28) 28) A) Yes B) No Answer: A Explanation: A) B) Find the zero of the linear function. 29) f(x) = x + 9 29) A) - 9 B) 0 C) 18 D) 9 Answer: A Explanation: A) B) C) D) Solve the problem using your calculator. 30) The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). What is the correlation coefficient? Cost 9 2 3 4 2 5 9 10 Number 85 52 55 68 67 86 83 73 30) A) 0.235 B) 0.246 C) - 0.071 D) 0.708 Answer: D Explanation: A) B) C) D) 12

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    Find the slope and the y - intercept of the line with the given equation. 31) 2 x + 5 y = 26 31) A) - 2 5 ; 0, 26 5 B) 2 1 2 ; 0, 5 26 C) - 2 1 2 ; 0, 5 26 D) 2 5 ; 0, 26 5 Answer: A Explanation: A) B) C) D) Find the domain and range of the function represented in the graph. 32) 32) A) Domain: ( - 1, 2]; Range: [ 1 , 3 ) B) Domain: [ - 2, 1]; Range: [ 0 , 3 ] C) Domain: [ - 2, 1); Range: [ - 2 , 5 ) D) Domain: ( - 2, 1]; Range: [ 0 , 3 ) Answer: D Explanation: A) B) C) D) Graph the function. 33) f(x) = x + 4 33) 13

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    A) B) C) D) Answer: B Explanation: A) B) C) D) Solve the problem. 34) A construction company builds a swimming pool with a perimeter of 58 m. The length is 11 m more than the width. Find the dimensions of the swimming pool? 34) A) 20 m × 11 m B) 15 m × 9 m C) 25 m × 9 m D) 20 m × 9 m Answer: D Explanation: A) B) C) D) 14

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    Find the domain of the function. 35) f(x) = x 4 - 2 x 3 + 7 3 x 2 - 5 x - 28 35) A) {x| x J 4 }, or ( - Q , 4 ) 1 ( 4 , Q ) B) x|x J - 4 and x J 7 3 , or ( - Q , - 4 ) 1 - 4 , 7 3 1 7 3 , Q C) x|x J - 7 3 and x J 4 , or - Q , - 7 3 1 - 7 3 , 4 1 ( 4 , Q ) D) x|x J - 7 3 , or - Q , - 7 3 1 - 7 3 , Q Answer: C Explanation: A) B) C) D) Solve the problem. 36) Company A rents copiers for a monthly charge of $ 180 plus 12 cents per copy. Company B rents copiers for a monthly charge of $ 360 plus 6 cents per copy. What is the number of copies above which Company A's charges are the higher of the two? 36) A) 6000 copies B) 1500 copies C) 3100 copies D) 3000 copies Answer: D Explanation: A) B) C) D) Use substitution to determine whether the given ordered pair is a solution of the given equation. 37) ( - 6 , - 57 ); y = 8 x - 9 37) A) Yes B) No Answer: A Explanation: A) B) Determine the equation of the line described. Put answer in the slope - intercept form, if possible. 38) Through ( 9 , - 7 ), perpendicular to 4 x - 3 y = 57 38) A) y = 3 4 x + 1 4 B) y = - 3 4 x C) y = - 3 4 x - 1 4 D) y = - 4 3 x + 1 Answer: C Explanation: A) B) C) D) Use substitution to determine whether the given ordered pair is a solution of the given equation. 39) ( 5 , 3 ); 2 x - 2 y = 16 39) A) Yes B) No Answer: B Explanation: A) B) 15

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    Find the slope of the line. 40) 40) A) - 1 2 B) 2 C) 1 2 D) - 2 Answer: B Explanation: A) B) C) D) Use substitution to determine whether the given ordered pair is a solution of the given equation. 41) ( 2 , 4 ); y = - 5 x + 14 41) A) Yes B) No Answer: A Explanation: A) B) Solve the problem. 42) An airplane leaves Los Angeles for Denver at a speed of 420 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed of 470 mph. When they meet, how far are they from Denver? 42) A) 286 mi B) 115 mi C) 57 mi D) 338 mi Answer: D Explanation: A) B) C) D) 16

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    Express the data in the graph as ordered pairs, letting the first coordinate represent the year and the second coordinate the amount. 43) Winter Vacation: The length of the average winter vacation is decreasing. 9 8.8 8.6 8.5 8.1 8 7.8 7.6 7 6 2003 2004 2005 2006 2007 2008 Year 43) A) (2003, 8.6 ), (2004, 8.8 ), (2005, 8.1 ), (2006, 8.5 ), (2007, 7.8 ), (2008, 7.6 ) B) ( 8.6 , 2003), ( 8.8 , 2004), ( 8.5 , 2005), ( 8.1 , 2006), ( 7.6 , 2007), ( 7.8 , 2008) C) (2003, 8.8 ), (2004, 8.6 ), (2005, 8.5 ), (2006, 8.1 ), (2007, 7.8 ), (2008, 7.6 ) D) ( 8.8 , 2003), ( 8.6 , 2004), ( 8.5 , 2005), ( 8.1 , 2006), ( 7.8 , 2007), ( 7.6 , 2008) Answer: C Explanation: A) B) C) D) Find the zero of the linear function. 44) f(x) = 13 - x 44) A) - 26 B) 1 C) 13 D) - 13 Answer: C Explanation: A) B) C) D) Find the requested measurement. 45) The points ( - 2, - 3) and ( - 2, 6 ) are the endpoints of the diameter of a circle. Find the length of the radius of the circle. 45) A) 4.5 B) 4 C) 5.5 D) 5 Answer: A Explanation: A) B) C) D) 17

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    Find the slope of the line containing the given points. 46) ( 2 , - 5 ) and ( 0.46 , - 5 ) 46) A) 0.46 - 2 B) not defined C) 0 D) 2 - 0.46 Answer: C Explanation: A) B) C) D) Find the domain and range of the function represented in the graph. 47) 47) A) Domain: [0, 7 ]; Range: [0, 5 ] B) Domain: [0, 4 ]; Range: [0, 2 ] C) Domain: [0, 2 ]; Range: [0, 4 ] D) Domain: ( - Q , 2 ]; Range: [ 4 , Q ] Answer: C Explanation: A) B) C) D) Is the following correspondence a function? 48) 48) A) Yes B) No Answer: A Explanation: A) B) 18

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    Find the coordinates of the points shown on the graph. 49) 49) A) A: ( 7 , 4 ), B: ( 4 , - 6 ) B) A: ( 7 , 4 ), B: ( 4 , 4 ) C) A: ( 4 , 30 ), B: ( 4 , - 6 ) D) A: ( 7 , 4 ), B: ( - 6 , 4 ) Answer: D Explanation: A) B) C) D) 50) 50) A) E: ( - 6 , - 6 ), G: ( 2 , - 6 ) B) E: ( 2 , 4 ), G: ( - 6 , - 5 ) C) E: ( - 6 , 2 ), G: ( - 6 , - 5 ) D) E: ( - 6 , 2 ), G: ( - 5 , - 6 ) Answer: D Explanation: A) B) C) D) 19

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    Solve the equation. 51) 2(x + 5 ) = 5 - 4(x + 5 ) 51) A) 25 B) - 25 6 C) 25 6 D) 1 6 Answer: B Explanation: A) B) C) D) Find an equation for the circle. 52) Endpoints of a diameter ( - 1 , - 5 ), ( - 1 , 5 ) 52) A) x 2 + (y + 5 ) 2 = 1 B) (x + 1 ) 2 + y 2 = 25 C) (x + 5 ) 2 + y 2 = 1 D) (x + 1 ) 2 + y 2 = 5 Answer: B Explanation: A) B) C) D) Evaluate as requested. 53) A graph of a function f is shown below. Find f( 1 ). 53) A) 0 B) - 2 C) 1 D) 2 Answer: A Explanation: A) B) C) D) 20

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    Determine whether the graph is the graph of a function. 54) 54) A) Yes B) No Answer: B Explanation: A) B) Solve the problem. 55) If an object is dropped from a tower of unknown height, the velocity of the object after t seconds can be obtained by multiplying t by 32 and adding 10 to the result. Therefore, you can express V as a linear function of t. Find the domain of this function. 55) A) [1, 4] B) [0, Q ) C) ( - 1, Q ) D) ( - Q , Q ) Answer: B Explanation: A) B) C) D) Graph the equation using the slope and the y - intercept. 56) 2 x - y = 0 56) 21

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    A) B) C) D) Answer: C Explanation: A) B) C) D) 22

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    Find the domain and range of the function represented in the graph. 57) 57) A) Domain: [ - 6 , - 1 ); Range: [ - 3, 2) B) Domain: [ - 3, 2) ; Range: [ - 6 , - 1 ) C) Domain: ( - Q , 3 ]; Range: (2, Q ) D) Domain: ( - 3, 2 ]; Range: ( - 6 , - 1 ] Answer: B Explanation: A) B) C) D) 23

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    Solve and give interval notation for the solution set. Then graph the solution set. 58) 1 - 4x L 6 or 1 - 4x < 2 58) A) - 5 4 , - 1 4 B) g Q , - 1 4 1 5 4 , Q C) - 5 4 , 1 4 D) g Q , - 5 4 1 - 1 4 , Q Answer: D Explanation: A) B) C) D) Graph the equation. 59) y = 1 2 x - 3 59) 24

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    A) B) C) D) Answer: A Explanation: A) B) C) D) Find the midpoint of the segment having the given endpoints. 60) ( - 2 , - 4 ) and ( 9 , 0 ) 60) A) ( - 11 , - 4 ) B) ( 7 , - 4 ) C) 7 2 , - 2 D) - 11 2 , - 2 Answer: C Explanation: A) B) C) D) Graph the equation. 25

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    61) y = - 3 x - 3 61) A) B) C) D) Answer: C Explanation: A) B) C) D) 26

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    Solve and graph the solution set. 62) 9 x - 10 K 8 x - 12 62) A) {x|x > 9 } or ( 9 , Q ) B) {x|x L - 2 } or [ - 2 , Q ) C) {x|x < 9 } or ( - Q , 9 ) D) {x|x K - 2 } or ( - Q , - 2 ] Answer: D Explanation: A) B) C) D) Tell whether or not the relation is a function. 63) {( - 6 , - 6 ), ( - 6 , - 3 ), ( - 1 , - 6 ), ( 6 , - 2 ), ( 7 , 6 )} 63) A) Yes B) No Answer: B Explanation: A) B) Determine the equation of the line described. Put answer in the slope - intercept form, if possible. 64) Through ( - 1 , 5 ), perpendicular to - 5 x - 2 y = 15 64) A) y = 1 2 x + 15 2 B) y = - 2 5 x + 27 5 C) y = 2 5 x + 27 5 D) y = 5 2 x + 5 2 Answer: C Explanation: A) B) C) D) 27

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    Find the slope of the line containing the given points. 65) ( 8 , - 4 ) and ( 8 , - 8 ) 65) A) 1 4 B) not defined C) 0 D) - 3 4 Answer: B Explanation: A) B) C) D) Plot the two points given by the ordered pairs. 66) A(0, 1 ), B( - 4 , 2 ) 66) A) B) 28

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    C) D) Answer: D Explanation: A) B) C) D) Find the domain of the function. 67) f(x) = x + 9 67) A) {x|x L 9 }, or [ 9 , Q ) B) {x|x L - 9 }, or [ - 9 , Q ) C) {x|x J 9 }, or ( - Q , 9 ) 1 ( 9 , Q ) D) all real numbers, or ( - Q , Q ) Answer: B Explanation: A) B) C) D) Plot the two points given by the ordered pairs. 68) A( - 5 , 0), B( - 5 , 4 ) 68) 29

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    A) B) C) D) Answer: C Explanation: A) B) C) D) 30

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