MATH 1015 Final Exam Review Rev 02/2018

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1 MATH 1 Final Exam Review Rev 0/018 ============================================================================== 1)Find the domain and range for the function. 1) A) D: {-, -,, }; R: {-, -, 3, } B) D: {-, -, -, 0,,, }; R: {-, -, -1,, 3, } C) D: {-, -, -,,, }; R: {-, -, -1,, 3, } D) D: {-, -, -1,, 3, }; R: {-, -, -,,, } )Find the domain and range for the function. ) A) D: [-, ]; R: [-3, 0] B) D: (-, ]; R: [0, 3] C) D: [-3, 0]; R: [-, ] D) D: [0, 3]; R: (-, ] 3) Given f(x) = (x + ), find f(1). A) 1 B) 9 C) -9 D) 3) ) Given f(x) = x - 3x - 3, find f(-). A) 1 B) C) 1 D) ) ) Given f(x) = x - x - 1, find f 1 ) A) - 7 B) 7 C) 1 1 D)

2 ) If y = f(x), find f(1). ) A) - B) 0 C) D) 1 7) If y = f(x), find f(-3). 7) A) -1 B) 1 C) - D) 8) Employees of a publishing company received an increase in salary of % plus a bonus of $00. Let S(x) = 1.0x + 00 represent the new salary in terms of the previous salary x. Find and interpret S(1,000). 8) A) $,900; If an employee's old salary was $,900, then his/her new salary was $1,000 after the increase and bonus. B) $1,30; If an employee's old salary was $1,000, then his/her new salary was $1,30 after the increase and bonus. C) $1,73; If an employee's old salary was $1,73, then his/her new salary was $1,000 after the increase and bonus. D) $1,00; If an employee's old salary was $1,000, then his/her new salary was $1,00 after the increase and bonus.

3 9) The function E(x) = 0.009x x x gives the approximate total earnings of a company, in millions of dollars, where x = 0 corresponds to 00, x = 1 corresponds to 007, and so on. This model is valid for the years from 00 to 0. Determine the earnings for 007. Round to two decimal places if necessary. 9) A) $.0 million B) $1.87 million C) $.07 million D) $.7 million ) The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: M(x) = 1x - x. What rainfall produces the maximum number of mosquitoes? A) 8 in. B) in. C) 1 in. D) 0 in. ) 11) Determine a viewing window that will provide a complete graph of the function. y = 3x 3 - x + 18x ) A) [-, ] by [-00, 0] B) [-8, ] by [-0, 300] C) [-, ] by [-, ] D) [-3, ] by [-00, 0] 1)Graph. y = x + 3x - A) B) 1) C) D)

4 13)Graph. y = A) - x B) ) C) D) )Find the slope of the line. 1) - - A) -1 B) C) - D) 1 1)Find the slope of the line. 1) - - A) 0 B) 7 C) -7 D) undefined

5 1) Find the rate of change. Use appropriate units. 1) Value of Car in Thousands of Dollars Number of Years of Use A) $000 per year B) -$000 per year C) -$000 per year D) $000 per year 17)Find the x- and y-intercepts of the graph of the given equation, if they exist. Then graph the equation. x = - 17) A) x: none; y: (0, -) C) x: (-; 0); y: none B) x: none; y: (0, -) D) x: (-, 0); y: none

6 18)Find the x- and y-intercepts of the graph of the given equation, if they exist. Then graph the equation. 3x - 9y = 18 18) A) x: (, 0); y: (0,-) B) x: (, 0); y: (0, -) C) x: (-, 0); y: (0, ) - D) x: (-, 0); y: (0, ) ) The cost of tuition at a community college is given by C(x) = + 3x, where x is the number of credit hours. Interpret the slope of this function as a rate of change. A) The tuition at the community college increases by $ for each additional 3 credit hours. B) The number of credit hours increases by 3 for each increase of $ in tuition. C) The tuition at the community college increases by $3 for each additional credit hour. D) The tuition at the community college increases by $ for each additional credit hour. 19) 0) The cost of a rental car for the weekend is given by the function C(x) = x, where x is the number of miles driven. Find and interpret the C-intercept of the graph of this function. A) 19; There is a flat rate of $19 to rent a car in addition to the charge for each mile driven. B) 19; The cost of the rental car increases by $19 for each mile driven. C) 0.; There is a flat rate of $0. to rent a car in addition to the charge for each mile driven. D) 0.; The cost of the rental car increases by $0. for each mile driven. 0)

7 1) A boat is moving away from shore in such a way that at time t hours its distance from shore, in kilometers, is given by the linear function d(t) = 3.t +.1. What is the rate of change of the distance from shore? 1) A).1 m/s B) 3. m/s C).1 km/hr D) 3. km/hr ) The population of a small town can be modeled by P = -3t + 13,000, where t is the number of years since 0. Interpret the slope of the graph of this function as a rate of change. ) A) The population of the town is decreasing by 13,000 people per year. B) The population of the town is increasing by 3 people per year. C) The population of the town is increasing by 13,000 people per year. D) The population of the town is decreasing by 3 people per year. 3) In a certain town the annual consumption, b, of beef (in pounds per person) can be estimated by b = 3-0.t, where t is the number of years since 0. Find and interpret the b-intercept of the graph of this function. 3) A) 7; If this trend continues, the annual consumption of beef in this town will be zero pounds per person in the year 08. B) 7; The annual consumption of beef in this town was 7 pounds per person in 0. C) 3; If this trend continues, the annual consumption of beef in this town will be zero pounds per person in the year 0. D) 3; The annual consumption of beef in this town was 3 pounds per person in 0. ) Solve. x x = 3 ) A) -90 B) C) 90 D) - )Find the zero of f(x). f(x) = 1 3 x + 1 ) A) - 1 B) 1 C) - 1 D) 1 )Find the zero of f(x). f(x) = x + 1 ) A) B) 1 C) -1 D) - 7)Find the zero of f(x). f(x) = 1 x 7) A) - B) 0 C) D) does not exist 8)Find the zero of f(x). f(x) = -x 8) A) - B) 0 C) D) does not exist 7

8 9)Solve. S = πrh + πr for h A) h = S S - πr - 1 B) h = π(s - r) C) h = πr πr D) h = S - r 9) 30)Solve. A = 1 h(b 1 + b) for b1 30) A) b1 = A - hb h B) b1 = hb - A h C) b1 = A - hb h D) b1 = Ab - h h 31)Solve. A = P(1 + nr) for r A) r = Pn A - P B) r = A n C) r = P - A Pn D) r = A - P Pn 31) 3)Solve for y. x - y = 8 3) A) y = 1 x - 8 B) y = x - 8 C) y = x - 3 D) y = 1 x )Solve for y. 3x - y = - A) y = - 3 x + 3 B) y = 3 x + 3 C) y = 3x + 11 D) y = 3 x - 33) 3)The graph of a certain function y = f(x) and the zero of that function is given. Using this graph, find a) the x-intercept of the graph of y = f(x) and b) the solution to the equation f(x) = 0. 3) A) a. (0, -) b. x = 0 B) a. (-, 0) b. x = - C) a. (-, 0) b. x = 0 D) a. (0, -) b. x = - 8

9 3) The mathematical model C = 900x + 80,000 represents the cost in dollars a company has in manufacturing x items during a month. How many items were produced if costs reached $800,000? A) 800 items B) 711 items C) 978 items D) 799,0 items 3) 3) Mark has $7 to spend on salmon at $.00 per pound and/or chicken at $3.00 per pound. If he buys s pounds of salmon and c pounds of chicken, the equation s + 3c = 7 must be satisfied. How much salmon did Mark buy if he bought pounds of chicken? A) 17 lb B) 1 lb C) 1 lb D) 19 lb 3) 37) When going more than 38 miles per hour, the gas mileage of a certain car fits the model y = x where x is the speed of the car in miles per hour and y is the miles per gallon of gasoline. Based on this model, at what speed will the car average 1 miles per gallon? (Round to nearest whole number.) A) 19 mph B) 98 mph C) 73 mph D) 8 mph 37) 38) An average score of 90 for exams is needed for a final grade of A. John's first exam grades are 79, 89, 97, and 9. Determine the grade needed on the fifth exam to get an A in the course. A) 9 B) 90 C) 0 D) 8 38) 39) The future value of a simple interest investment is given by S = P(1 + rt), where P is the principal invested at a simple interest rate r for t years. What principal P must be invested for t = 3 months at the simple interest rate r = 1% so that the future value grows to $300. A) $.99 B) $03.7 C) $.90 D) $ ) 0)Find the linear function that is the best fit for the given data. Round decimal values to the nearest hundredth, if necessary. x y A) y =.8x -.7 B) y = -.8x +.7 C) y =.x -. D) y = -.x +. 0) 1) Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below. Find the linear function to model this data. Performance Attitude ) A) y = x B) y = x C) y = x D) y = x 9

10 ) The paired data below consist of the test scores of randomly selected students and the number of hours they studied for the test. Find a linear function that predicts a student's score as a function of the number of hours he or she studied. Hours 9 Score ) A) y = x B) y = x C) y = x D) y = x 3) The paired data below consist of the test scores of randomly selected students and the number of hours they studied for the test. The linear model for this data is y = x, where x is number of hours studied and y is score on the test. Use this model to predict the score on the test of a student who studies 13 hours. Hours 9 Score ) A) 81. B) 7. C) 8.8 D) 8. ) The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters). The linear model for this data is y = x, where x is temperature and y is growth in millimeters. Use this model to predict the growth of a plant if the temperature is. Temp Growth ) A) 7.09 mm B).0 mm C). mm D).1 mm )Solve. -(3a - 1) < -0a + 0 ) A) a < -0 B) a > -0 C) a > -7 D) a < -7 )Solve. Express the solution in interval notation. -x + 1-7x + 7. A) (-, ) B) (-, -) C) (-, ] D) [, ) ) 7)Solve. -0 < -x - A) 1 x B) 1 x < C) - < x -1 D) 1 < x < 7) 8)Solve. -13 < 3y + -1 A) - < y - B) - < y < - C) - y < - D) - y - 8) 9)Solve. -9 -c + 1 < - A) - < c -3 B) 3 < c C) - c < -3 D) 3 c < 9)

11 0)Solve. A) 9 x < 33 - < - x 7 C) - 9 x < 33 9 B) 9 < x < 33 D) - 9 x 33 0) 1)Solve x -11 1) A) < x 9 B) x 9 C) x < 9 D) < x < 9 ) Jim has gotten scores of 7 and 89 on his first two tests. What score must he get on his third test to keep an average of 80 or greater? A) At least 8 B) At least 78.7 C) At least 78 D) At least 83 ) 3) Jon has 93 points in his math class. He must have 8% of the 0 points possible by the end of the term to receive credit for the class. What is the minimum number of additional points he must earn by the end of the term to receive credit for the class? A) 8 points B) 7 points C) 0 points D) 7 points 3) ) Correct Computers, Inc. finds that the cost to make x laptop computers is C = 181x + 130,78, while the revenue produced from them is R = x (C and R are in dollars). What is the smallest whole number of computers, x, that must be sold for the company to show a profit? A) 33,00,30 computers B),8,3 computers C) 3 computers D) 3 computers ) ) DG's Plumbing and Heating charges $0 plus $70 per hour for emergency service. Bill remembers being billed just over $0 for an emergency call. How long to the nearest hour was the plumber at Bill's house? A) hours B) 1 hours C) 7 hours D) 1 hours ) ) Using the formula to find Fahrenheit (F) in terms of Celsius (C), F = 9 C + 3, find the range (to ) the nearest tenth) of the Fahrenheit temperature when the range of the Celsius temperature is between C and C, inclusive. A) Between 3. F and 18 F, inclusive B) Between 33.1 F and 3.8 F, inclusive C) Between 3. F and 0 F, inclusive D) Between 19. F and 3 F, inclusive 7) Assume that the mathematical model C(x) = 18x + represents the cost C, in hundreds of dollars, for a certain manufacturer to produce x items. How many items x can be manufactured while keeping costs between between $0,000 and $98,000? A) 380 < x < 70 B) 70 < x < 70 C) 0 < x < 70 D) 30 < x < 0 7) 11

12 8)Graph the quadratic equation on [-, ] by [-, ]. Does this window give a complete graph? f(x) = x + x - 8) A) No B) Yes C) Yes - D) Yes ) Write the equation of the quadratic function whose graph is shown. 9) 8 (1, ) (3, 0) A) y = (x - 1) + B) y = -(x + 1) + C) y = -(x - 1) + D) y = -(x - 1) + 1

13 0) Write the equation of the quadratic function whose graph is shown. 8 0) (, ) (3, -7) A) y = -(x - 3) - 7 B) y = (x - 3) - 7 C) y = (x + 3) - 7 D) y = -(x - 3) + 7 1)Give the coordinates of the vertex. y = (x - 9) + A) (-9, ) B) (-9, -) C) (9, ) D) (9, -) 1) )Give the coordinates of the vertexx. y = (x + 13) A) (0, 13) B) (-13, 0) C) (13, 0) D) (0, -13) ) 3)Give the coordinates of the vertex. y = 3x + 18x + A) (-1, -3) B) (-3, -1) C) (3, 1) D) (1, 3) 3) )Give the coordinates of the vertex. y = x - A) (0, ) B) (, 0) C) (0, -) D) (-, 0) ) )Determine the x-intercepts of the graph of y = x - x - ) A) (-1, 0), (-, 0) B) (-, 0), (3, 0) C) (-3, 0), (-, 0) D) (-3, 0), (, 0) )Determine the x-intercepts of the graph of y = -x + x + 3 ) A) (-7, 0), (, 0) B) (-3, 0), (-, 0) C) (-, 0), (7, 0) D) (, 0), (7, 0) 7)Determine the x-intercepts of the graph of f(x) = x - 0x + 1 7) A) (, 0), (1, 0) B) (1., 0), (3., 0) C) (-3., 0), (-1.,0) D) (-9, 0), (1, 0) 8)Determine the x-intercepts of the graph of g(x) = -x - 3x + 8) A) (-., 0), (1, 0) B) (-1, 0), (., 0) C) (-3, 0), (, 0) D) (-, 0), (, 0) 13

14 9) Sketch the complete graph of the function. y = 3x - 0x ) A) B) C) D) )Give the coordinates of the vertex and graph the equation in a window that includes the vertex. y = x - 0x + 1 A) Vertex: (30, -88) B) Vertex: (1, -390) 70) C) Vertex: (1, -3) D) Vertex: (-1, -3)

15 71)Give the coordinates of the vertex and graph the equation in a window that includes the vertex. y = - 0.x - 1x + 71) A) Vertex: (17., 7.) B) Vertex: (-3, 1) C) Vertex: (3, 1) D) Vertex: (-17., 7.) ) At Allied Electronics, production has begun on the X-1 Computer Chip. The total revenue function is given by R(x) = 8x - 0.3x and the total cost function is given by C(x) = 11x + 1, where x represents the number of boxes of computer chips produced. The total profit function, P(x), is such that P(x) = R(x) - C(x). Find P(x). 7) A) P(x) = -0.3x + 3x + 1 B) P(x) = 0.3x + 7x - C) P(x) = 0.3x + 3x - 3 D) P(x) = -0.3x + 7x ) John owns a hot dog stand. He has found that his profit is given by the equation P = -x + 8x + 79, where x is the number of hot dogs sold. How many hot dogs must he sell to earn the most profit? 73) A) hot dogs B) hot dogs C) 3 hot dogs D) 3 hot dogs 7) John owns a hot dog stand. His profit, in dollars, is given by the equation P(x) = P = -x + 1x +, where x is the number of hot dogs sold. What is the most he can earn? 7) A) $117 B) $3 C) $9 D) $7 1

16 7) Given the following revenue and cost functions, find the x-value that makes revenue a maximum. R(x) = 8x - x ; C(x) = 1x + 97 A) 17 B) 1 C) 18 D) 3 7) 7) Given the following revenue and cost functions, find the x-value that makes profit a maximum. (Recall that profit equals revenue minus cost.) R(x) = 8x - x ; C(x) = 1x + 9 A) 9. B) 18. C). D) 1. 7) 77) The profit for a product is given by p = x - x, where x is the number of units produced and sold. Graphically find the x-intercepts of this function to find how many units will give break-even (that is return a profit of zero). 77) A) 80 units B) or 80 units C) They will never break even. D) units 78) If a ball is thrown upward at feet per second from the top of a building that is 180 feet high, the height of the ball can be modeled by S = t - 1t feet, where t is the number of seconds after the ball is thrown. After how many seconds does the ball reach its maximum height? A) sec B). sec C) 1 sec D) sec 78) 79) If a ball is thrown upward at feet per second from the top of a building that is 180 feet high, the height of the ball can be modeled by S = t - 1t feet, where t is the number of seconds after the ball is thrown. What is the ball's maximum height? A) 37 ft B) 180 ft C) 8 ft D) ft 79) 80) Your company uses the quadratic model y = -.x + x to represent the average number of new customers who will be signed on (x) weeks after the release of your new service. How many new customers can you expect to gain in week 18? 80) A) 1 customers B) -8 customers C) 1 customers D) 19 customers 81) The polynomial function I(t) = -0.1t + 1.7t represents the yearly income (or loss) from a real estate investment, where t is time in years. After how many years does income begin to decline? 81) A) 8. yr B) 7. yr C) 17 yr D) yr 8)Solve. 0x + 33x + = 0 8) A) x =, x = B) x =, x = - C) x = -, x = - D) x = -, x = - 1

17 83)Solve. x - 9 = 0 A) ± B). C) 3 D) ±3 83) 8)Solve. y - 1 = 0 A) ± 3 B) 1 C) D) 1 8) 8)Solve. -7k - = -33 A) B) -1. C) ± D) ± 8) 8)Solve. y + 19y + 1 = 0 8) A) - 3, - 3 B) 3, - 3 C) -, - 1 D) 3, 3 87)Solve. z + 1z + 1 = 0 A) B) + C) ± 1 D) - ± 87) 88)Solve. p - p - = 0 88) A) 1 ± i 1 B) 1 ± 17 C) 1 ± 17 D) -1 ± 17 89)Solve. n = -1n ) A) - ± B) -1 ± 30 C) - ± 30 1 D) - ± 30 90) Approximate solutions to the equation. round your answers to three decimal places. x + 7x = - 90) A).193, B) -.307, C) , D) 0.3, ) Solve. x + 19 = 0 A) ±1 B) 1i C) -98i D) ±1i 91) 9)Solve. (7x - 1) + = 0 A) 1 ± 7 B) 1 7 ± 7 i C) 1 7 ± 7 i D) 7 ± 7i 9) 93)Solve. x - x + 13 = 0 A) - ± 3i B) ± 3i C), -1 D) ± i 93) 17

18 9)Solve. x + x + 9 = 0 9) A) 1 ± 3 B) 1 ± 3 i C) -1 ± 3 D) -1 ± 3 i 9)Solve. x x = - 7 9) A) 0, - 7 i B) -1 ± 1 i C) 1 ± 1 i D) 1 3 i, 0 9) A grasshopper is perched on a reed inches above the ground. It hops off the reed and lands on the ground about 7.9 inches away. During its hop, its height is given by the equation h = -0.3x + 1.7x +, where x is the distance in inches from the base of the reed, and h is in inches. How far was the grasshopper from the base of the reed when it was 3.7 inches above the ground? Round to the nearest tenth. 9) A) 0. in. B) 0.8 in. C). in. D) 7.9 in. 97) If an object is propelled upward from a height of feet at an initial velocity of feet per second, then its height after t seconds is given by the equation h = -1t + t +, where h is in feet. After how many seconds will the object reach a height of 18 feet? 97) A) 1 sec B) 8 sec C) sec D) sec 98) The function defined by D t = 13t - 73t gives the distance in feet that a car going approximately 0 mph will skid in t seconds. Find the time it would take for the car to skid 380 ft. Round to the nearest tenth. 98) A).3 sec B) 9.9 sec C) 8.9 sec D).1 sec 99) Assume that the elevation E, in feet, of a sag in a proposed route is given by E(x) = x - 0.x + 10, where x represents the horizontal distance in feet along the proposed route and 0 x 000. For what x-values is the elevation 00 feet? Round your answer to the nearest foot. 99) A) x = 39 ft or x = 99 ft B) x = 9 ft or x = 99 ft C) x = 39 ft or x = 98 ft D) x = 9 ft or x = 98 ft 0) If an amount of money, called the principal, P, is deposited into an account that earns interest at a rate r, compounded annually, then in two years that investment will grow to an amount A, given by the formula A = P(1 + r). If a principal amount of $00 grows to $.00 in two years, what is the interest rate? 0) A) 11% B) % C) 1% D) 8% 18

19 1)Graph. f(x) = A) 1 x + 1 B) 1) C) D) )Graph. y = x - 3 ) A) B) C) D)

20 3)Graph f(x) = 3, if x x, if x < 1 3) A) B) C) D) ) Graph f(x) = x, if x -3 -x, if x > -3 ) A) B) C) D)

21 ) Evaluate f(-) for f(x) = x, if x -1 x - 7, if x > -1 ) A) -9 B) - C) - D) ) Evaluate f() for f(x) = x + if x 0 - x if 0 < x < x if x ) A) B) C) D) -1 7) Evaluate f(-3) for f(x) = x - x -, if x -3 x, if x > -3 7) A) 1 B) C) -3 D) 17 8) For f(x) = - x -, find f(). A) -1 B) C) D) 1 8) 9) Suppose S varies directly as the cubed root of T, and that S = 1 when T =. Find T when S = 9. A) 1 B) C) 7 D) 3 9) 1) Suppose x varies inversely as y squared, and x = when y = 8. Find x when y =. A) 9 B) C) D) 7 1) 111) If money is invested for years, with interest compounded annually, the future value of the investment varies directly as the square of (1 + r), where r is the annual interest rate. If the future value of the investment is $79.0 when the interest rate is %, what rate gives a future value of $77.7? 111) A) 0.0% B) % C) % D) 0% 11) Suppose a car rental company charges $11 for the first day and $ for each additional or partial day. Let S(x) represent the cost of renting a car for x days. Find the value of S(3.). 11) A) $31 B) $81 C) $37 D) $31 1

22 113) The charges for renting a moving van are $0 for the first 0 miles and $ for each additional mile. Assume that a fraction of a mile is rounded up. a. Determine the cost of driving the van 8 miles. b. Find a symbolic representation for a function f that computes the cost of driving the van x miles, where 0 < x 0. (Hint: express f as a piecewise-constant function.) A) a. $70; b. f(x) = 0 if 0 < x (x + 0) if 0 < x 0 113) B) a. $70; b. f(x) = C) a. $70; b. f(x) = 0 if 0 < x (x + 0) if 0 < x 0 0 if 0 < x (x - 0) if 0 < x 0 D) a. $130; b. f(x) = 0 if 0 < x 0 0x + (x - 0) if 0 < x 0 11) In Country X, the average hourly wage in dollars from 190 to 0 can be modeled by 11) f(x) = 0.079(x - 190) if 190 x < (x - 198) if 198 x 0 Use f to estimate the average hourly wages in 19, 198, and 00. A) $3.3, $0.3, $.79 B) $0.7, $3.03, $.79 C) $0.7, $.33, $.79 11) The number of people present at a stadium holding a big rock concert can be estimated with the following function: y = 13x x +, where y is the number of people present and x is the amount of time after 3:00 P.M. on the day of the concert. Predict the number of people present at 7:00PM. A) 3,901 people B) 38,70 people C) 3,00 people D) 3,09 people 11) 11) The number of mice in an old barn after the cats are removed can be roughly estimated with the following function: y =.3x x + 1, where y is the number of mice and x is the number of weeks since a cat lived in the barn. Predict the number of mice there will be in ten weeks if you get rid of the cat in the barn. A) mice B) 18 mice C) 1 mice D) 17 mice 11) 117) A study in a small town showed that the percent of residents who have college degrees can be modeled by the function P = 33x 0.33, where x is the number of years since 0. Use numerical or graphical methods to find when the model predicts that the percent will be. A) 019 B) 00 C) 018 D) )

23 118) The number G of gears a machine can make varies directly as the time T it operates. If it can make 1980 gears in 7 hours, how many gears can it make in 3 hours? 118) A) 1990 gears B) 0.0 gears C) 8.8 gears D) 88.7 gears 119) The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. Suppose the the intensity is 8000 units at a distance of miles. What will the intensity be at a distance of miles? Round your answer to the nearest unit. 119) A) 83 units B) 87 units C) 91 units D) 889 units ) The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a -m beam can support 30 kg. How many kilograms can a -m beam support? ) A) 0.19 kg B) kg C) 7 kg D) 17 kg 11)Sketch the graph of the pair of functions. Use a dashed line for g(x). f(x) = x, g(x) = - (x + ) + 11) A) B) C) - D)

24 1) The graph of y = -(x - ) + 8 can be obtained from the graph of y = x by : 1) A) shifting horizontally units to the right; vertically stretching by a factor of ; reflecting across the x-axis, and shifting vertically 8 units in the upward direction. B) shifting horizontally units to the right; vertically stretching by a factor of 8; reflecting across the y-axis, and shifting vertically units in thedownward direction. C) shifting horizontally units to the left; vertically stretching by a factor of ; reflecting across the x-axis, and shifting vertically 8 units in the upward direction. D) shifting horizontally units to the right; vertically stretching by a factor of 8; reflecting across the x-axis, and shifting vertically units in the upward direction. 13) The graph of y = -(x + ) - 8 can be obtained from the graph of y = x by: 13) A) shifting horizontally units to the right; vertically stretching by a factor of ; reflecting across the x-axis, and shifting vertically 8 units in the downward direction. B) shifting horizontally units to the right; vertically stretching by a factor of ; reflecting across the x-axis, and shifting vertically 8 units in the upward direction. C) shifting horizontally units to the left; vertically stretching by a factor of 8; reflecting across the x-axis, and shifting vertically units in the downward direction. D) shifting horizontally units to the left; vertically stretching by a factor of ; reflecting across the x-axis, and shifting vertically 8 units in the downward direction. 1) Write the equation of the graph after the indicated transformation(s). The graph of y = x is shifted 8 units to the left and units downward. 1) A) y = (x - 8) - B) y = (x + 8) - C) y = (x + ) - 8 D) y = (x - ) + 8 1) Write the equation of the graph after the indicated transformation(s). The graph of y = x is shifted 3 units to the right. This graph is then vertically stretched by a factor of and reflected across the x-axis. Finally, the graph is shifted 7 units upward. 1) A) y = -(x + 7) + 3 B) y = -(x + 3) + 7 C) y = -(x - 3) + 7 D) y = -(x - 3) - 7 1) Write the equation of the graph after the indicated transformation(s). The year y when sales were s million dollars for a particular electronics company can be modeled by the radical equation y = 1. s - - 7, where y = 1 represents 0, and so on. Use the model to predict the sales for 01 to the nearest tenth of a million. 1) A) $11. million B) $. million C) $119. million D) $118. million 17) f(x) = x -, g(x) = x - 9 Find (f - g)(x). 17) A) x - 1 B) x + 3 C) -x - 3 D) x - 1

25 18) f(x) = 9x - 1, g(x) = x - Find (f g)(x). A) 1x - 1x - B) x + C) x - 11x + D) x - 1x + 18) 19) f(x) = 8x - 9x, g(x) = x - x - 7 Find f g (x). 19) A) 8x x + 1 B) 8 - x 7 C) 8x - 9x x - x - 7 D) 8x ) f(x) = 7x -, g(x) = 1 x Find (f - g)(x). 130) A) 7x - x - 1 x B) 7x - x - x C) 7x - - x D) 7x - x + x 131) For f(x) = x - 9 and g(x) = x + 7, what is the domain of f g (x)? 131) A) [7, ) B) [0, ) C) (-7, 7) D) (-7, ) 13) For f(x) = x - and g(x) = x - 7, what is the domain of f/g? A) [, 7) (7, ) B) (, 7) (7, ) C) [, ) D) [0, 7) (7, ) 13) 133) If f(x) = x + 3 and g(x) = x + 1x +, evaluate (f g)(-). A) -0 B) 0 C) -1 D) ) 13) Given f(x) = -x + and g(x) = x + 9, find (g f)(x). A) 30x + B) -30x - 7 C) -30x + 1 D) -30x + 13) 13) Given f(x) = 1 - x and g(x) = 3x + 8, find (f g)(x). A) 3-3x B) 7 + 3x C) 7-3x D) x ) 13) Find (g f)(-17) when f(x) = x - 7 and g(x) = x ) A) - 19 B) 18 C) -9 D) ) Find (f g)(-3) when f(x) = x + and g(x) = -x - x - 1. A) -911 B) 178 C) 139 D) )

26 138)Evaluate (f g)(-). 138) y = g(x) y = f(x) A) 0 B) -3 C) 3 D) 139) The monthly total cost of producing clock radios is given by C(x) = 3, x, where x is the number of radios produced per month. Find the monthly average cost function. A) C (x) = C) C (x) = 3, x x x 3, x B) C (x) = 3, x D) C (x) = x(3, x) 139) ) Let C(x) = x be the cost to manufacture x items. Find the average cost per item to produce 80 items. A) $37 B) $80 C) $31 D) $9 ) 11) At Allied Electronics, production has begun on the X-1 Computer Chip. The total revenue function is given by R(x) = x - 0.3x and the total cost function is given by C(x) = 3x + 1, where x represents the number of boxes of computer chips produced. The total profit function, P(x), is such that P(x) = R(x) - C(x). Find P(x). A) P(x) = 0.3x + 0x - B) P(x) = -0.3x + 3x - 1 C) P(x) = 0.3x + 3x - 8 D) P(x) = -0.3x + 0x ) 1) The cost of manufacturing clocks is given by C(x) = + 1x - x. Also, it is known that in t hours the number of clocks that can be produced is given by x = t, where 1 t 1. Express C as a function of t. A) C(t) = + t - 0t B) C(t) = + t - 0t C) C(t) = + 1t + t D) C(t) = + 1t - 1) 13)Find the inverse of the function. f(x) = x - 3 A) f-1(x) = x + 3 B) f-1(x) = x ) C) f-1(x) = x + 3 D) Not a one-to-one function

27 1)Find the inverse of the function. f(x) = -9 - x 1) A) f -1 (x) = -7 - x B) f -1 (x) = 9 - x C) f -1 (x) = x D) f -1 (x) = x 1)Find the inverse of the function. f(x) = 8 x + 7 A) Not a one-to-one function B) f-1(x) = 7 + 8x x C) f-1(x) = x 7 + 8x D) f-1(x) = -7x + 8 x 1) 1)The graph of the function y = f(x) is given. On the same axes, sketch the graph of f -1 (x). Use a dashed line for the inverse function. 1) A) C) B) D)

28 17)The graph of the function y = f(x) is given. On the same axes, sketch the graph of f -1 (x). Use a dashed line for the inverse function. 17) A) C) B) D) ) Let f(x) = 1 x. Find f(-3). 18) A) -1 B) C) 1 1 D) 1 19) Let f(x) = 3 (1 - x). Find f(). 19) A) -9 B) 7 C) 1 7 D) 1 9 ) Let f(x) =.8e -.3x. Find f(0.8), rounded to four decimal places. A) B) -0.7 C) D) 0.7 ) 8

29 11)Graph. f(x) = (x - 1) 11) A) B) C) D) )Graph. f(x) = 3e - x 1) A) C) B) D)

30 13) In September 1998 the population of the country of West Goma in millions was modeled by f(x) = 17.9e x. At the same time the population of East Goma in millions was modeled by g(x) = 1.e 0.018x. In both formulas x is the year, where x = 0 corresponds to September Assuming these trends continue, estimate the year when the population of West Goma will equal the population of East Goma. A) 0 B) 011 C) 198 D) 13 13) 1) In September 1998 the population of the country of West Goma in millions was modeled by f(x) = 1.1e x. At the same time the population of East Goma in millions was modeled by g(x) = 1.7e 0.013x. In both formulas x is the year, where x = 0 corresponds to September Assuming these trends continue, estimate what the population will be when the populations are equal. A) 1 million B) 1 million C) 1 million D) 1 million 1) 1) The growth in the population of a certain rodent at a dump site fits the exponential function A(t)= 708e 0.0t, where t is the number of years since Estimate the population in the year 000. A) 7 B) 97 C) 9 D) 7 1) 1) A computer is purchased for $00. Its value each year is about 77% of the value the preceding year. Its value, in dollars, after t years is given by the exponential function V(t) = 00(0.77) t. Find the value of the computer after 8 years. A) $8.18 B) $39.70 C) $7,70.00 D) $.08 1) 17)Write the logarithmic equation in exponential form. log w Q = 7 17) A) Q 7 = w B) w 7 = Q C) 7 w = Q D) Q w = 7 18) Write the logarithmic equation in exponential form. y = log (11x) A) y = 11x B) 11x y = C) y = 11x D) 11x = y 18) 19) Write the logarithmic equation in exponential form. y = ln (-x) 19) A) -x y = e B) e y = -x C) e y = - x D) e-x = y )Write in logarithmic form. p = 18 t A) log18 p = t B) logp 18 = t C) logt 18 = p D) log18 t = p ) 11)Write in logarithmic form. 8 3x = y A) log8 y = 3x B) logy 8 = 3x C) logy 3x = 8 D) log8 3x = y 11) 30

31 1) Evaluate. Round the answer to four decimal places. log 377 A) 3.70 B) C) 8.30 D) ) 13) Evaluate. Round the answer to four decimal places. ln A) 0.00 B) C) D) ) 1) Evaluate. Round the answer to four decimal places. log (-3) A) B) C) D) Does not exist 1) 1)Evaluate. log 9 1 1) A) B) 0 C) 9 D) 1 1)Evaluate. log ) A) - B) 9 C) D) -9 17)Evaluate. log ) A) 3 B) -3 C) -81 D) 81 18)Graph. f(x) = log (x - ) 18) A) B) C) D)

32 19)Find the inverse of the function. f(x) = 9 x + 3 A) f -1 (x) = log9(x - 3) B) f -1 (x) = log9(x + 3) 19) C) f -1 (x) = log9(x + 9) D) f -1 (x) = log9(x - 9) 170)Use the properties of logarithms to evaluate the expression. logaa 3 A) 3loga a B) 3 C) 1 D) a 3 170) 171)Use the properties of logarithms to evaluate the expression. ln e A) 1 B) ln e C) D) e 171) 17) The sales of a new product (in items per month) can be approximated by S(x) = log(3t + 1), where t represents the number of months after the item first becomes available. Find the number of items sold per month 3 months after the item first becomes available. A) 37 items per month B) 7 items per month C) 17 items per month D) 7 items per month 17) 173) Coyotes are one of the few species of North American animals with an expanding range. The future population of coyotes in a region of Mississippi can be modeled by the equation P = + 18 ln(11t + 1), where t is time in years. Use the equation to determine when the population will reach. Round to the nearest tenth when necessary. A) 9. years B) 9.3 years C),98. years D) 9. years 173) 17)Solve. Round to three decimal places. 3 x = 3 A).037 B) 7.7 C).8 D) ) 17)Solve. Round to three decimal places. (3x - 3) = 0 A) 1.0 B) 1. C).333 D) ) 17)Solve. Round to three decimal places. (9-3x) = 1 A) 3 B) C) D) - 17) 177)Evaluate. Approximate to three decimal places. log (9.3) 177) A) B). C) D) ) Solve. Give an exact solution. log3 x = - 178) A) 1 8 B) 1 C) 1 9 D) - 3

33 179)Solve log x = A) - 11 B) -1 C) -11 D) no solution 179) 180) Solve. log(x + 18) = A) 0 B) 18 C) D) 8 180) 181) Determine a window which gives a complete graph of the polynomial function. f(x) = x + x 3 - x - 3x - A) [-3, 3] by [-3, ] B) [-3, 3] by [-, ] C) [-, ] by [-, 1] D) [-, ] by [-, -] 181) 18) Determine a window which gives a complete graph of the polynomial function. f(x) = 3x 3 - x + 18x - 7 A) [-, ] by [-, ] B) [-3, ] by [-00, 0] C) [-, ] by [-00, 0] D) [-8, ] by [-0, 300] 18) 183) Use the given graph of the polynomial function to estimate the x-intercepts. 183) A) (-9, 0), (-1, 0) B) (-9, 0), (3, 0) C) (-1, 0), (3, 0) D) (-9, 0), (-1, 0), (3, 0) 33

34 18) Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and whether the polynomial function is cubic or quartic. 18) - - A) Negative; Quartic B) Negative; Cubic C) Positive; Quartic D) Positive; Cubic 18) Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and whether the polynomial function is cubic or quartic. 18) - - A) Positive; Quartic B) Negative; Cubic C) Positive; Cubic D) Negative; Quartic 18) State the degree and leading coefficient of the polynomial function. f(x) = 8(x + 3)(x 8-3) A) Degree: 8; leading coefficient: 1 B) Degree: 8; leading coefficient: 8 C) Degree: 9; leading coefficient: 8 D) Degree: 9; leading coefficient: -8 18) 187) State the degree and leading coefficient of the polynomial function. f(x) = 8(x + ) (x - ) 187) A) Degree: ; leading coefficient: 8 B) Degree: ; leading coefficient: 1 C) Degree: ; leading coefficient: 8 D) Degree: ; leading coefficient: 1 3

35 188)Graph. y = -x + 0.x x - 1x - 1 A) B) 188) C) D) ) Choose the graph that satisfies the given conditions. Polynomial of degree 3 with three distinct x-intercepts and a positive leading coefficient A) B) 189) C) D) 3

36 190) Choose the graph that satisfies the given conditions. Cubic polynomial with two distinct x-intercepts and a positive leading coefficient A) B) 190) C) D) 191) Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest hundredth. y = 3x 3 - x - x + 191) A) Local max: (-0.8, 3.3); local min: (1.38, -.01) B) Local max: (-.01, 1.38); local min: (3.3, -0.8) C) Local max: (-0.8, 3.8); local min: (1.38, -.1) D) Local max: (-0., 3.1); local min: (1., -.97) 19) The polynomial R(x) = -0.03x x + 00 approximates the shark population in a particular area, where x is the number of years from 198. Use a graphing calculator to describe the shark population from the years 198 to 0. 19) A) The population increases. B) The population remains stable. C) The population decreases. D) Not enough information. 193) Ariel, a marine biologist, models a population P of crabs, t days after being left to reproduce, with the function P(t) = t t +.t Assuming that this model continues to be accurate, when will this population become extinct? (Round to the nearest day.) A) 11 days B) 7 days C) 707 days D) 911 days 193) 3

37 19)Solve. (3x + )(x - ) (x + ) = 0 19) A) -, 1, - B) - 3, -,, - C) 3, -, D) - 3,, - 19)Solve. (x + 7) ( - x) = 0 19) A) 7, - B) -7, C) - 7, D) - 7, 7, -, 19)Solve. x 3-8x + 11x + 0 = 0 A),, -1 B) -, -, 1 C),, -1 D) -, -, 0 19) 197)Solve. x - 1x + 3 = 0 A) B) -, C) D) -, 197) 198)Use the graph of the polynomial function f(x) to solve f(x) = ) A) -, 0, 1 B) -1, C) -, 1, 8 D) -, 1 199) If the price for a product is given by p = 0 - x, where x is the number of units sold, then the revenue is given by R = px = 0x - x 3. How many units must be sold to give zero revenue? A) 0, 0 B) 0 C) 0, 0 D) 0 199) 00) The Cool Company determines that the supply function for its basic air conditioning unit is S(p) = p 3 and that its demand function is D(p) = 0-0.p, where p is the price. Determine the price for which the supply equals the demand. A) $1.3 B) $1.8 C) $.3 D) $.8 00) 37

38 Answer Key Testname: MATH 1 FE REVIEW REV SP18 1) C ) C 3) B ) C ) A ) C 7) D 8) B 9) A ) A 11) D 1) D 13) B 1) D 1) A 1) C 17) D 18) B 19) C 0) A 1) D ) D 3) D ) B ) A ) D 7) B 8) B 9) C 30) C 31) D 3) D 33) B 3) B 3) A 3) B 37) C 38) B 39) D 0) D 1) C ) B 3) A ) D ) D ) D 7) B 8) A 9) B 0) C 1) B ) A 3) B ) C ) A ) C 7) D 8) D 9) D 0) B 1) C ) B 3) B ) C ) B ) C 7) B 8) A 9) D 70) C 71) B 7) D 73) C 7) B 7) A 7) A 77) B 78) A 79) D 80) C 81) A 8) C 83) D 8) A 8) D 8) A 87) D 88) B 89) D 90) C 91) D 9) C 93) B 9) D 9) C 9) C 97) C 98) C 99) D 0) B 1) B ) B 3) A ) B ) C ) B 7) D 8) A 9) C 1) C 111) C 11) D 113) C 11) B 11) D 11) B 117) C 118) D 119) D ) D 11) B 1) A 13) D 1) B 1) C 1) C 17) B 18) D 19) C 130) B 131) D 13) A 133) C 13) D 13) C 13) C 137) D 138) B 139) A ) C 11) B 1) B 13) A 1) D 1) D 1) B 17) A 18) D 19) C ) D 11) C 1) D 13) B 1) D 1) C 1) D 17) B 18) C 19) B ) A 11) A 1) A 13) B 1) D 1) B 1) A 17) B 18) B 19) A 170) B 171) C 17) A 173) B 17) C 17) A 17) C 177) B 178) C 179) C 180) D 181) B 18) B 183) C 18) B 18) A 18) C 187) C 188) B 189) B 190) D 191) A 19) A 193) B 19) D 19) C 19) C 197) B 198) D 199) A 00) B 38