MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use point-b-point plotting to sketch the graph of the equation. 1) = A) (, 8) (0, 3) - - (-6, -3) - - B) (-6, 9) (0, 3) - - (, -) - - 1

2 C) (-6, 3) - - (0, -3) - (, -8) D) - (, ) (0, -3) (-6, -9) - Answer: A ) =

3 A) B) C) D) Answer: D 3

4 Determine whether the graph is the graph of a function. 3) A) function B) not a function ) A) function B) not a function Answer: A ) A) function B) not a function

5 Determine whether the relation represents a function. If it is a function, state the domain and range. 6) 7) A) function domain:{, 18, 6, 3} range: {, 9, 13, 17} B) function domain: {, 9, 13, 17} range: {, 18, 6, 3} C) not a function Bob Ann Dave carrots peas squash A) function domain: {Bob, Ann, Dave} range: {carrots, peas, squash} B) function domain: {carrots, peas, squash} range: {Bob, Ann, Dave} C) not a function 8) {(-1, -3), (-, -), (-, 0), (, ), (1, )} A) function domain: {-3, -, 0,, } range: {-1,, -, 1} B) function domain: {-1,, -, 1} range: {-3, -, 0,, } C) not a function 9) {(-, ), (-1, ), (0, 1), (1, ), (3, )} A) function domain: {,, 1, } range: {-, -1, 0, 1, 3} B) function domain: {-, -1, 0, 1, 3} range: {,, 1, } C) not a function

6 Determine whether the function is linear, constant, or neither ) = A) Linear B) Constant C) Neither Answer: A 11) = A) Linear B) Constant C) Neither 1) = π 3 A) Linear B) Constant C) Neither 13) - 1 = 0 A) Linear B) Constant C) Neither Use point-b-point plotting to sketch the graph of the equation. 1) f() =

7 A) B) C) D)

8 The graph of a function f is given. Use the graph to answer the question. 1) Use the graph of f given below to find f(). - A) 0 B) -0 C) 1 D) Find the function value. - 16) Find f(-8) when f() = 7-3. A) 199 B) -18 C) D) 31 17) f() = A) 13 6 B) ; f() C) 9 D)

9 18) Given that f() = -, find f(t + ). A) t + 18t + 16 B) t + t - 6 C) t - 18t + 16 D) 3t + 6 Answer: A SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 19) If g() = , find g(-), g(1), and g 3. Answer: -7, -1, ) For f(t) = 3t + and g(t) = - t, find f(3) - g(-3) + g(0). Answer: 3 1) For f(t) = 3 - t, find Answer: - f(a + h) - f(a). h MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Compute and simplif the difference quotient ) f() = + 7 A) 1-7h + 1 B) + 7 C) + h + 7 D) + h+ 7 Determine the domain of the function. 3) f() = A) All real numbers ecept 9 7 B) No solution C) All real numbers D) 9 7 f( + h) - f(), h 0. h 9

10 ) f() = - A) All real numbers ecept B) < C) No solution D) All real numbers Answer: A ) f() = 3 - A) 3 B) No solution C) All real numbers ecept 3 D) < 3 Answer: A 6) f() = 8 3 A) All real numbers ecept 0 B) No solution C) < 0 D) All real numbers Answer: A SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 7) Onl one of the following functions has domain which is not equal to all real numbers. State which function and state its domain. (A) h() = (B) f() = Answer: f() = 8 - (C) g() = + 7 has domain all real numbers ecept = MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine if the equation specifies a function with independent variable. If so, find the domain. If not, find a value of to which there corresponds more than one value of. 8) - = 9 A) A function with domain R B) Not a function; for eample, when =, = ±1 9) = + A) A function with domain R B) Not a function; for eample, when =, then = ±1 Answer: A

11 30) = A) A function with domain all real numbers ecept = 0 B) Not a function; for eample, when =, = ±1 Answer: A 31) + 3 = A) A function with domain all real numbers ecept = -3 B) Not a function; for eample, when =, = ±3 Answer: A 3) + = 9 A) A function with domain R B) Not a function; for eample, when = 0, = ±3 33) - = 9 A) A function with domain all real numbers ecept = B) Not a function; for eample, when =, = ± Solve the problem. 3) The function F described b F() = can be used to estimate the height, in centimeters, of a woman whose humerus (the bone from the elbow to the shoulder) is cm long. Estimate the height of a woman whose humerus is cm long. Round our answer to the nearest four decimal places. A) cm B) cm C) cm D).1600 cm Answer: A 3) The function M described b M() = can be used to estimate the height, in centimeters, of a male whose humerus (the bone from the elbow to the shoulder) is cm long. Estimate the height of a male whose humerus is cm long. Round our answer to the nearest four decimal places. A) m B) cm C) cm D) cm Answer: D 36) To estimate the ideal minimum weight of a woman in pounds multipl her height in inches b and subtract 130. Let W = the ideal minimum weight and h = height. W is a linear function of h. Find the ideal minimum weight of a woman whose height is 6 inches. A) lb B) 118 lb C) 378 lb D) 130 lb 11

12 37) The point at which a compan's costs equals its revenue is the break-even. C represents cost, in dollars, of units of a product. R represents the revenue, in dollars, for the sale of units. Find the number of units that must be produced and sold in order to break even. C = 1 + 1,000 R = A) 1,000 B) 6000 C) 800 D) 38) The function P, given b P(d) = 1 d + 1, gives the pressure, in atmospheres (atm), at a depth d, in feet, under 33 the sea. Find the pressure at 00 feet. Round our answer to the nearest whole number. A) 7 atm B) 01 atm C) 00 atm D) 8 atm Answer: A 39) To estimate the ideal minimum weight of a woman in pounds multipl her height in inches b and subtract 130. Let W = the ideal minimum weight and h = height. Epress W as a linear function of h. A) W(h) = 130h + B) W(h) = h C) W(h) = 130 D) W(h) = (h + 130) Provide an appropriate response. 0) In a profit-loss analsis, point where revenue equals cost. A) inflection point B) turning point C) break-even point D) profit-loss point SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) Let T be the set of teachers at a high school and let S be the set of students enrolled at that school. Determine which of the following correspondences define a function. Eplain. (A) A student corresponds to the teacher if the student is enrolled in the teacher's class. (B) A student corresponds to ever teacher of the school. hoice (A) defines a function. To each element (student) of the first set (or domain), there corresponds eactl one element (teacher) of the second set (or range). Choice (B) does not define a function. An element (student) of the first set (or domain) corresponds to more that one element (teacher) of the second set (or range). 1

13 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Give the domain and range of the function. ) f() = + 6 A) Domain: all real numbers; Range: [6, ) B) Domain: [6, ); Range: all real numbers C) Domain: all real numbers; Range: [-, ) D) Domain: [0, ); Range: [0, ) Answer: A 3) g() = - A) Domain: [, ); Range: all real numbers B) Domain: all real numbers; Range: [-3, ) C) Domain: all real numbers; Range: [-, ) D) Domain: [0, ); Range: [0, ) ) h() = - A) Domain: all real numbers; Range: (-, -] B) Domain: (-, 0]; Range: all real numbers C) Domain: [0, ); Range: [0, ) D) Domain: all real numbers; Range: (-, 0] Answer: D ) s() = -6 - A) Domain: (-, -6) (-6, ); Range: (-, 0) (0, ) B) Domain: ( -6, ); Range: (-, 0] C) Domain: (-, -6]; Range: [0, ) D) Domain: all real numbers; Range: [0, ) 6) r() = A) Domain: all real numbers; Range: [- 6, ) B) Domain: all real numbers; Range: [0, ) C) Domain: [- 6, ); Range: all real numbers D) Domain: all real numbers; Range: all real numbers Answer: A Provide an appropriate response. 7) How can the graph of f() = be obtained from the graph of =? A) Shift it horizontall -1 units to the left. Reflect it across the -ais. B) Shift it horizontall 1 units to the left. Reflect it across the -ais. C) Shift it horizontall 1 units to the left. Reflect it across the -ais. D) Shift it horizontall 1 units to the right. Reflect it across the -ais. 13

14 8) How can the graph of f() = -( -1 ) 6 be obtained from the graph of =? A) Shift it horizontall 1 units to the left. Reflect it across the -ais. Shift it 6 units up. B) Shift it horizontall 1 units to the right. Reflect it across the -ais. Shift it 6 units down. C) Shift it horizontall 1 units to the right. Reflect it across the -ais. Shift it 6 units up. D) Shift it horizontall 1 units to the right. Reflect it across the -ais. Shift it 6 units up. Write an equation for a function that has a graph with the given transformations. 9) The shape of = is shifted units to the left. Then the graph is shifted 7 units upward. A) f() = 7 + B) f() = C) f() = D) f() = Answer: D 0) The shape of = is verticall stretched b a factor of, and the resulting graph is reflected across the -ais. A) f() = - B) f() = C) f() = ( - ) D) f() = ( - ) Answer: A SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) The following graph represents the result of appling a sequence of transformations to the graph of a basic function. Identif the basic function and describe the transformation(s). Write the equation for the given graph asic function is f() = ; shift right units, shift up units. f() = ( - ) + 1

15 ) The following graph represents the result of appling a sequence of transformations to the graph of a basic function. Identif the basic function and describe the transformation(s). Write the equation for the given graph asic function is f() = ; reflect over the -ais, shift left units, shift down units. f() = MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the function. 3) f() = - if < 1 if A) - - 1

16 B) - - C) - - D)

17 ) f() = if < - 3 if - - A) - - B)

18 C) - - D) - - Answer: A ) Assume it costs cents to mail a letter weighing one ounce or less, and then 0 cents for each additional ounce or fraction of an ounce. Let L() be the cost of mailing a letter weighing ounces. Graph = L(). Use the interval (0, ]. A) Cost (in dollars) Weight (in ounces) 18

19 B) C) Cost (in dollars) Cost (in dollars) Weight (in ounces) D) Cost (in dollars) Weight (in ounces) 1 3 Weight (in ounces) 19

20 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - 3 if < 6) If f() =, what is the definition of g(), the function whose graph is obtained b shifting f()'s if graph right units and down 1 unit? Answer: g() = - 9 < 7 ( - ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 7) A retail chain sells washing machines. The retail price p() (in dollars) and the weekl demand for a particular model are related b the function p() = 6 -, where (i) Describe how the graph of the function p can be obtained from the graph of one of the si basic functions: =, =, = 3, =, = 3, or =. (ii) Sketch a graph of function p using part (i) as an aid. A) (i) The graph of the basic function = is reflected in the -ais and verticall epanded b a factor of. (ii)

21 B) (i) The graph of the basic function = is reflected in the -ais, verticall epanded b a factor of, and shifted up 6 units. (ii) C) (i) The graph of the basic function = is verticall epanded b a factor of 6, and shifted up units. (ii) D) (i) The graph of the basic function = is verticall epanded b a factor of, and shifted up 6 units. (ii)

22 8) The following table shows a recent state income ta schedule for married couples filing a joint return in State X. State X Income Ta SCHEDULE I - MARRIED FILING JOINTLY If taable income is Over But not over Ta due is $0 $0,000.% of taable incomes $0,000 $70,000 $3700 plus 6.7% of ecess over $0,000 $70,000 $387 plus 7.0% of ecess over $70,000 (i) Write a piecewise definition for the ta due T() on an income of dollars. (ii) Graph T(). (iii) Find the ta due on a taable income of $0,000. Of $9, A) (i) T() = (ii) 0.0 if 0 0, if 0,000 < 70, if > 70, (iii) $38; $

23 B) (i) T() = (ii) 0.0 if 0 0, if 0,000 < 70, if > 70, (iii) $30; $ C) (i) T() = (ii) 0.0 if 0 0, if 0,000 < 70, if > 70, (iii) $37; $

24 D) (i) T() = (ii) 0.0 if 0 0, if 0,000 < 70, if > 70, (iii) $07; $ ) The average weight of a particular species of frog is given b w() = 98 3, , where is length (with legs stretched out) in meters and w() is weight in grams. (i) Describe how the graph of function w can be obtained from one of the si basic functions: =, =, = 3, = function w using part (i) as an aid., = 3, or =. (ii) Sketch a graph of

25 A) (i) The graph of the basic function = is verticall epanded b a factor of 98. (ii) B) (i) The graph of the basic function = 3 is reflected on the -ais and is verticall epanded b a factor of 98. (ii) C) (i) The graph of the basic function = 3 is verticall epanded b a factor of 98. (ii)

26 D) (i) The graph of the basic function = 3 is verticall epanded b a factor of 98. (ii) Answer: D Find the -intercept(s) if the eist. 60) = 0 A) -1, - B), - C) 1, D), - Answer: A 61) 6 = A) 1 B) 0 C) 0, 7 D) 7 6

27 For the given function, find each of the following: (A) Intercepts (B) Verte (C) Maimum or minimum (D) Range 6) f() = ( + 3) - A) (A) -intercepts: -, -1; -intercept: (B) Verte (3, -) (C) Minimum: - (D) - B) (A) -intercepts: 1, ; -intercept: (B) Verte (-3, -) (C) Minimum: - (D) - C) (A) -intercepts: -, -1; -intercept: (B) Verte (-3, -) (C) Maimum: - (D) - D) (A) -intercepts: -, -1; -intercept: (B) Verte (-3, -) (C) Minimum: - (D) - Answer: D 63) g() = ( - ) - 9 A) (A) -intercepts: - 1, ; -intercept: - (B) Verte (, -9) (C) Minimum: -9 (D) -9 B) (A) -intercepts: - 1, ; -intercept: - (B) Verte (-, -9) (C) Minimum: -9 (D) -9 C) (A) -intercepts: - 1, ; -intercept: - (B) Verte (, -9) (C) Maimum: -9 (D) -9 D) (A) -intercepts: -, 1; -intercept: - (B) Verte (, -9) (C) Minimum: -9 (D) -9 Answer: A 7

28 6) m() = -( + 3) + A) (A) -intercepts: -, -1; -intercept: - (B) Verte (3, -) (C) Maimum: (D) B) (A) -intercepts: 1, ; -intercept: - (B) Verte (-3, ) (C) Maimum: (D) C) (A) -intercepts: -, -1; -intercept: - (B) Verte (-3, ) (C) Maimum: (D) D) (A) -intercepts: -, -1; -intercept: - (B) Verte (-3, ) (C) Minimum: (D) 6) n() = -( - 1) + 9 A) (A) -intercepts: -, ; -intercept: 8 (B) Verte (-1, -9) (C) Maimum: 9 (D) 9 B) (A) -intercepts: -, ; -intercept: 8 (B) Verte (1, 9) (C) Minimum: 9 (D) 9 C) (A) -intercepts: -, ; -intercept: 8 (B) Verte (1, 9) (C) Maimum: 9 (D) 9 D) (A) -intercepts: -, ; -intercept: 8 (B) Verte (1, 9) (C) Maimum: 9 (D) 9 Answer: D 8

29 Find the verte form for the quadratic function. Then find each of the following: (A) Intercepts (B) Verte (C) Maimum or minimum (D) Range 66) f() = A) Standard form: f() = ( + 1) - (A) -intercepts: - 3, 1; -intercept: -3 (B) Verte (1, -) (C) Minimum: - (D) - B) Standard form: f() = ( + 1) - (A) -intercepts: - 3, 1; -intercept: -3 (B) Verte (-1, -) (C) Minimum: - (D) - C) Standard form: f() = ( - 1) - (A) -intercepts: -1, 3; -intercept: -3 (B) Verte (-1, -) (C) Minimum: - (D) - D) Standard form: f() = ( - 1) - (A) -intercepts: - 3, 1; -intercept: -3 (B) Verte (-1, -) (C) Maimum: - (D) - 9

30 67) g() = A) Standard form: g() = ( + 1) - (A) -intercepts: -3, 1; -intercept: -3 (B) Verte (1, -) (C) Minimum: - (D) - B) Standard form: g() = ( - 1) - (A) -intercepts: - 1, 3; -intercept: -3 (B) Verte (-1, -) (C) Minimum: - (D) - C) Standard form: g() = ( + 1) - (A) -intercepts: - 1, 3; -intercept: -3 (B) Verte (1, -) (C) Maimum: - (D) - D) Standard form: g() = ( - 1) - (A) -intercepts: - 1, 3; -intercept: -3 (B) Verte (1, -) (C) Minimum: - (D) - Answer: D 30

31 68) m() = A) Standard form: m() = -( - 3) + 1 (A) -intercepts: -, -; -intercept: -8 (B) Verte (-3, 1) (C) Minimum: 1 (D) 1 B) Standard form: m() = -( + 3) + 1 (A) -intercepts: -, -; -intercept: -8 (B) Verte (-3, 1) (C) Maimum: 1 (D) 1 C) Standard form: m() = -( - 3) + 1 (A) -intercepts:, ; -intercept: -8 (B) Verte (-3, 1) (C) Maimum: 1 (D) 1 D) Standard form: m() = -( + 3) + 1 (A) -intercepts: -, -; -intercept: -8 (B) Verte (3, -1) (C) Maimum: 1 (D) 1 31

32 69) n() = A) Standard form: n() = -( + ) + 1 (A) -intercepts: -3, - 1; -intercept: -3 (B) Verte (, 1) (C) Maimum: 1 (D) 1 B) Standard form: n() = -( - ) + 1 (A) -intercepts: 1, 3; -intercept: -3 (B) Verte (, 1) (C) Maimum: 1 (D) 1 C) Standard form: n() = -( - ) + 1 (A) -intercepts: 1, 3; -intercept: -3 (B) Verte (-, -1) (C) Maimum: 1 (D) 1 D) Standard form: n() = -( + ) + 1 (A) -intercepts: 1, 3; -intercept: -3 (B) Verte (, 1) (C) Minimum: 1 (D) 1 Determine whether there is a maimum or minimum value for the given function, and find that value. 70) f() = A) Minimum: 0 B) Maimum: - C) Maimum: D) Minimum: Answer: D 71) f() = A) Minimum: 9 B) Maimum: - 9 C) Minimum: -9 D) Minimum: 0 Find the range of the given function. Epress our answer in interval notation. 7) f() = A) (-, ] B) [3, ) C) [ -, ) D) (-, -3] 3

33 73) f() = A) (-, -3] B) (-, -] C) [-3, ) D) [, ) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 7) Find the verte and the maimum or minimum of the quadratic function f() = b first writing f in standard form. State the range of f and find the intercepts of f. Answer: f() = -( + ) + 9 ; verte: (-, 9); maimum: f(-) = 9; Range of f = { 9} ; -intercept: (0, ); -intercepts: (-, 0), (1, 0). 7) Graph f() = and indicate the maimum or minimum value of f(), whichever eists Answer: Ma f() =

34 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write an equation for the graph in the form = a( - h) + k, where a is either 1 or -1 and h and k are integers. 76) A) = ( + ) + B) = ( - ) - C) = ( - ) - D) = ( - ) - Answer: D 77) A) = ( + ) - B) = -( - ) - C) = -( + ) + D) = ( + ) + Solve graphicall to two decimal places using a graphing calculator. 78) > 0 A) -.7 < < 0.96 B) < -.7 or > 0.96 C) < or >.7 D) < <.7 3

35 79) A) < <.7 B) -.7 < < 0.96 C) < -.7 or > 0.96 D) < or >.7 Answer: A Solve the equation graphicall to four decimal places. 80) Let f() = , find f() = 3. A).078 B) 0.79 C) 0.79,.078 D) No solution 81) Let f() = , find f() = -. A) No solution B) -1.77, 9.77 C) D) ) Let f() = , find f() =. A) No solution B).000 C).700 D).000,.700 Answer: A For the following problem, (i) graph f and g in the same coordinate sstem; (ii) solve f() = g() algebraicall to two decimal places; (iii) solve f() > g() using parts i and ii; (iv) solve f() < g() using parts i and ii. 83) f() = -0.8( - 8), g() = ;

36 A) (i) f is the curve, g is the line (ii) 0.61, 7.0 (iii) 0.61 < < 7.0 (iv) 0 < 0.61 or 7.0 < 8 B) (i) f is the curve, g is the line (ii) 0.8, 7.98 (iii) 0.8 < < 7.98 (iv) 0 < 0.8 or 7.98 < 8 36

37 C) (i) f is the curve, g is the line (ii) 0.8, 6.9 (iii) 0.8 < < 6.9 (iv) 0 < 0.8 or 6.9 < 8 D) (i) f is the curve, g is the line (ii) 0.61, 7.98 (iii) 0.61 < < 7.98 (iv) 0 < 0.61 or 7.98 < 8 Solve the problem. 8) In economics, functions that involve revenue, cost and profit are used. Suppose R() and C() denote the total revenue and the total cost, respectivel, of producing a new high-tech widget. The difference P() = R() - C() represents the total profit for producing widgets. Given R() = and C() = , find the equation for P(). A) P() = B) P() = C) P() = D) P() = Answer: A 37

38 8) In economics, functions that involve revenue, cost and profit are used. Suppose R() and C() denote the total revenue and the total cost, respectivel, of producing a new high-tech widget. The difference P() = R() - C() represents the total profit for producing widgets. Given R() = and C() = , find P(0). A) 000 B) 313 C) 1687 D) ) A professional basketball plaer has a vertical leap of 37 inches. A formula relating an athlete's vertical leap V, in inches, to hang time T, in seconds, is V= 8T. What is his hang time? Round to the nearest tenth. A) 0.8 sec B) 1 sec C) 0.9 sec D) 0.6 sec 87) Under certain conditions, the power P, in watts per hour, generated b a windmill with winds blowing v miles per hour is given b P(v) = 0.01v 3. Find the power generated b 18-mph winds. A) 8.3 watts per hour B).86 watts per hour C) watts per hour D) 87.8 watts per hour Answer: D 88) The U. S. Census Bureau compiles data on population. The population (in thousands) of a southern cit can be approimated b P() = , where corresponds to the ears after 190. In what calendar ear was the population about 80,00? A) 000 B) 196 C) 19 D) 1960 Answer: D 89) Assume that a person's critical weight W, defined as the weight above which the risk of death rises h 3 dramaticall, is given b W(h) =, where W is in pounds and h is the person's height in inches Find the tcritical weight for a person who is 6 ft 11 in. tall. Round to the nearest tenth. A) 1. lb B) 377. lb C) lb D) 1. lb 38

39 90) The polnomial gives the approimate total earnings of a compan, in millions of dollars, where represents the number of ears since This model is valid for the ears from 1996 to 000. Determine the earnings for 000. Round to decimal places. A) $.6 million B) $.36 million C) $.03 million D) $.8 million Use the REGRESSION feature on a graphing calculator. 91) The average retail price in the Spring of 000 for a used Camaro Z8 coupe depends on the age of the car as shown in the following table. Age, Price, 18,3 1,9 13,68 11,80, Find the quadratic model that best estimates this data. Round our answer to whole numbers. A) = , B) = ,790 C) = - 76 D) = ,669 Answer: D 9) As the number of farms has decreased in South Carolina, the average size of the remaining farms has grown larger, as shown below. AVERAGE ACREAGE YEAR PER FARM 1900 ( = 0) 19 ( = ) ( = 0) 0 Let represent the number of ears since Use a graphing calculator to fit a quadratic function to the data. Round our answer to five decimal places. A) = B) = C) = D) = Answer: A 39

40 93) Since 198 funeral directors have been regulated b the Federal Trade Commission. The average cost of a funeral for an adult in a Midwest cit has increased, as shown in the following table. AVERAGE COST YEAR OF FUNERAL 1980 $ $ $ $ $ $ 001 $ 30 Let represent the number of ears since Use a graphing calculator to fit a quartic function to the data. Round our answer to five decimal places. A) = B) = C) = D) = Solve the problem. 300t 9) The population P, in thousands, of Faetteville is given b P(t) = t, where t is the time, in months. Find + 7 the population at 9 months. A) 0,000 B) 30, 769 C) 7988 D) 1, 976 Answer: D 9) If the average cost per unit C() to produce units of plwood is given b C() = 0, what is the unit cost for + 0 units? A) $3.00 B) $.00 C) $80.00 D) $.00 Answer: D 96) Suppose the cost per ton,, to build an oil platform of thousand tons is approimated b C() = 1,00 +. What is the cost per ton for = 30? A) $ B) $67.03 C) $16.67 D) $.00 0

41 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 97) The financial department of a compan that produces digital cameras arrived at the following price-demand function and the corresponding revenue function: p() = R() = p() = (9. - 6) price-demand revenue function The function p() is the wholesale price per camera at which million cameras can be sold and R() is the corresponding revenue (in million dollars). Both functions have domain 1 1. The also found the cost function to be C() = (in million dollars) for manufacturing and selling cameras. Find the profit function and determine the approimate number of cameras, rounded to the nearest hundredths, that should be sold for maimum profit. Answer: P() = , must sell approimatel 6.69 million cameras. 98) The financial department of a compan that manufactures portable MP3 plaers arrived at the following dail cost equation for manufacturing MP3 plaers per da: C() = The average cost per unit at a production level of plaers per da is C() = C(). (A) Find the rational function C. (B) Graph the average cost function on a graphing utilit for 00. (C) Use the appropriate command on a graphing utilit to find the dail production level (to the nearest integer) at which the average cost per plaer is a minimum. What is the minimum average cost (to the nearest cent)? Answer: (A) C() = 0 (B) (C) 39; $18.6 1

42 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. For the polnomial function find the following: (i) Degree of the polnomial; (ii) All intercepts; (iii) The intercept. 99) = + A) (i) 1 (ii) (iii) B) (i) 1 (ii) - (iii) C) (i) 1 (ii) (iii) D) (i) 1 (ii) - (iii) 0) = - 9 A) (i) 1 (ii) 3 (iii) -9 B) (i) 1 (ii). (iii) -9 C) (i) (ii) -, (iii) -9 D) (i) (ii) -3, 3 (iii) -9 Answer: D

43 1) = A) (i) (ii) -6, (iii) -1 B) (i) (ii) -6, 1 (iii) -1 C) (i) (ii) 6, (iii) -1 D) (i) (ii) 6, - (iii) -1 Answer: A ) = A) (i) (ii) 6, -3 (iii) 18 B) (i) (ii) 3, -6 (iii) -18 C) (i) (ii) -3, -6 (iii) -18 D) (i) (ii) 6, 3 (iii) 18 Answer: A 3) = ( + 7)( + 7)( + ) A) (i) 3 (ii) -7, -7, - (iii) -1 B) (i) 3 (ii) -7, -7, - (iii) 98 C) (i) 3 (ii) 7, 7, (iii) 98 D) (i) 3 (ii) 7, 7, (iii) 1 3

44 ) f() = ( 6 + 7)( + 9) A) (i) 16 (ii) 7, 9 (iii) 63 B) (i) 60 (ii) 7, 9 (iii) -63 C) (i) 16 (ii) none (iii) 63 D) (i) 60 (ii) none (iii) -63 The graph that follows is the graph of a polnomial function. (i) What is the minimum degree of a polnomial function that could have the graph? (ii) Is the leading coefficient of the polnomial negative or positive? ) - - A) (i) (ii) Negative B) (i) (ii) Positive C) (i) 3 (ii) Negative D) (i) 3 (ii) Positive Answer: D

45 6) - - A) (i) 3 (ii) Positive B) (i) (ii) Negative C) (i) 3 (ii) Negative D) (i) (ii) Positive Answer: D 7) A) (i) (ii) Positive B) (i) 3 (ii) Negative C) (i) 3 (ii) Positive D) (i) (ii) Negative

46 8) A) (i) 1 (ii) Negative B) (i) 1 (ii) Positive C) (i) (ii) Negative D) (i) (ii) Positive Answer: A 9) A) (i) (ii) Negative B) (i) 3 (ii) Negative C) (i) (ii) Positive D) (i) 3 (ii) Positive 6

47 Provide an appropriate response. 1) What is the maimum number of intercepts that a polnomial of degree can have? A) 9 B) 11 C) D) Not enough information is given. 111) What is the minimum number of intercepts that a polnomial of degree 11 can have? Eplain. A) 0 because a polnomial of odd degree ma not cross the ais at all. B) 1 because a polnomial of odd degree crosses the ais at least once. C) 11 because this is the degree of the polnomial. D) Not enough information is given. 11) What is the minimum number of intercepts that a polnomial of degree 8 can have? Eplain. A) 8 because this is the degree of the polnomial. B) 1 because a polnomial of even degree crosses the ais at least once. C) 0 because a polnomial of even degree ma not cross the ais at all. D) Not enough information is given. For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find an vertical or horizontal asmptotes for the graph; (iv) Sketch an asmptotes as dashed lines. Then sketch the graph of = f(). 113) f() =

48 A) (i) intercept: -; intercept: (ii) Domain: all real numbers ecept -1 (iii) Vertical asmptote: = -1; horizontal asmptote: = 1 (iv) B) (i) intercept: 0; intercept: 0 (ii) Domain: all real numbers ecept 1 (iii) Vertical asmptote: = 1; horizontal asmptote: = 1 (iv) C) (i) intercept: ; intercept: (ii) Domain: all real numbers ecept 1 (iii) Vertical asmptote: = 1; horizontal asmptote: = 1 (iv)

49 D) (i) intercept: 0; intercept: 0 (ii) Domain: all real numbers ecept -1 (iii) Vertical asmptote: = -1; horizontal asmptote: = 1 (iv) Answer: A 11) f() = A) (i) intercept: 3; intercept: 3 (ii) Domain: all real numbers ecept (iii) Vertical asmptote: = ; horizontal asmptote: = 1 (iv)

50 B) (i) intercept: -3; intercept: 3 (ii) Domain: all real numbers ecept - (iii) Vertical asmptote: = -; horizontal asmptote: = 1 (iv) C) (i) intercept: ; intercept: 3 (ii) Domain: all real numbers ecept (iii) Vertical asmptote: = ; horizontal asmptote: = 1 (iv) D) (i) intercept: -; intercept: 3 (ii) Domain: all real numbers ecept - (iii) Vertical asmptote: = -; horizontal asmptote: = 1 (iv) Answer: A 0

51 3 11) f() = A) (i) intercept: 0; intercept: 0 (ii) Domain: all real numbers ecept - (iii) Vertical asmptote: = -; horizontal asmptote: = -3 (iv) B) (i) intercept: 0; intercept: 0 (ii) Domain: all real numbers ecept (iii) Vertical asmptote: = ; horizontal asmptote: = -3 (iv)

52 C) (i) intercept: 0; intercept: 0 (ii) Domain: all real numbers ecept (iii) Vertical asmptote: = ; horizontal asmptote: = 3 (iv) D) (i) intercept: 0; intercept: 0 (ii) Domain: all real numbers ecept - (iii) Vertical asmptote: = -; horizontal asmptote: = 3 (iv) ) f() =

53 A) (i) intercept: 3 ; intercept: - 3 (ii) Domain: all real numbers ecept (iii) Vertical asmptote: = ; horizontal asmptote: = - (iv) B) (i) intercept: - 3 ; intercept: - 3 (ii) Domain: all real numbers ecept - (iii) Vertical asmptote: = -; horizontal asmptote: = - (iv) C) (i) intercept: - 3 ; intercept: - 3 (ii) Domain: all real numbers ecept - (iii) Vertical asmptote: = -; horizontal asmptote: = - (iv)

54 D) (i) intercept: 3 ; intercept: - 3 (ii) Domain: all real numbers ecept (iii) Vertical asmptote: = ; horizontal asmptote: = - (iv) For the rational function below (i) Find an intercepts for the graph; (ii) Find an vertical and horizontal asmptotes for the graph; (iii) Sketch an asmptotes as dashed lines. Then sketch a graph of f ) = A) (i) intercept: (ii) horizontal asmptote: = 0; vertical asmptotes: = and = - (iii)

55 B) (i) intercept: - 6 (ii) horizontal asmptote: = 0 (iii) C) (i) intercept: - 6 (ii) horizontal asmptote: = 0; vertical asmptotes: = 1 and = -1 (iii) D) (i) intercept: - (ii) horizontal asmptote: = 0; vertical asmptotes: = and = - (iii) Sketch the graph of the function.

56 ) f() = A) 8 6 B) C)

57 D) Answer: D 119) f() = A) 8 6 B)

58 C) D) Answer: A Find the equation of an horizontal asmptote. ) f() = A) = 9 B) = 0 C) = 7 D) None 11) f() = + - A) = - B) = C) = 1 D) None 8

59 1) f() = A) None B) = -8 C) = 8 D) = 6 Answer: A Find the equations of an vertical asmptotes ) f() = + - A) = -1, = B) = 1, = - C) = D) = 1, = - Answer: D 1) f() = - 0 ( - 3)( + ) A) = 3, = - B) =, = - C) = 3, = - D) = -3 Answer: A 1) f() = A) = 7, = -3 B) = -7, = 3 C) = 7 D) None ) f() = + 6 A) = 3, = -3 B) = 6 C) = -6 D) None Answer: D 9

60 Write an equation for the lowest-degree polnomial function with the graph and intercepts shown in the figure. 17) A) f() = B) f() = C) f() = D) f() = ) A) f() = B) f() = C) f() = D) f() =

61 19) A) f() = B) f() = C) f() = D) f() = Solve the problem. 130) Financial analsts in a compan that manufactures ovens arrived at the following dail cost equation for manufacturing ovens per da: C() = The average cost per unit at a production level of ovens per da is C() = C()/. (i) Find the rational function C. (ii) Sketch a graph of C() for 1. (iii) For what dail production level (to the nearest integer) is the average cost per unit at a minimum, and what is the minimum average cost per oven (to the nearest cent)? HINT: Refer to the sketch in part (ii) and evaluate C() at appropriate integer values until a minimum value is found. 61

62 A) (i) C() = (ii) (iii) 61 units; $133.9 per oven B) (i) C() = (ii) (iii) units; $88.86 per oven C) (i) C() = (ii) (iii) units; $8.93 per oven 6

63 D) (i) C() = (ii) (iii) units; $18.61 per oven Graph the function. 131) f() = A)

64 B) C) D)

65 13) f() = ( + ) A) B) C)

66 D) ) f() = A)

67 B) C) D)

68 13) f() = A) B)

69 C) D) ) f() =

70 A) B) C)

71 D) Answer: A -6 Solve the equation. 136) Solve for : 3 (1 + ) = 7 A) 3 B) 1 C) -1 D) 9 137) Solve for : = 8 + A) - B) -1 C) 1 D) 138) Solve for : (e ) e = e A) {6, } B) {} C) {-6, -} D) {6} Answer: A 139) Solve for t: e -0.07t = 0.0 Round our answer to four decimal places. A).31 B) C) D).796 Answer: D 71

72 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. ) In the table below, the amount of the U.S. minimum wage is listed for selected ears. U.S. Minimum Wage Year Wage $1.1 $1.0 $.00 $3. $3.3 $3.80 $. $.7 $.1 Find an eponential regression model of the form = a b, where represents the U.S. minimum wage ears after Round a and b to four decimal places. According to this model, what will the minimum wage be in 00? In 0? Answer: = (1.09 ); $7.; $9.30 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 11) Hi-Tech UnWater begins a cable TV advertising campaign in Miami to market a new water. The percentage of the target market that bus water is estimated b the function w(t) = 0(1 - e -0.0t ), t represents the number of das of the campaign. After how long will 90% of the target market have bought the water? A) 3 das B) 11 das C) 90 das D) das 1) The number of books in a communit college librar increases according to the function B = 700e0.03t, where t is measured in ears. How man books will the librar have after 8 ear(s)? A),7 B) 6 C) 700 D) 913 Answer: D 13) Since life epectanc has increased in the last centur, the number of Alzheimer's patients has increased dramaticall. The number of patients in the United States reached million in 000. Using data collected since 000, it has been found that the data can be modeled b the eponential function =.199 (1.031), where is the ears since 000. Estimate the Alzheimer's patients in 0. Round to the nearest tenth. A).8 million B) 7.8 million C) 8.0 million D) 3.9 million 7

73 1) A sample of 800 grams of radioactive substance decas according to the function A(t) = 800e -0.08t, where t is the time in ears. How much of the substance will be left in the sample after ears? Round to the nearest whole gram. A) 1 gram B) 800 grams C) 60 grams D) 9 grams 1) The number of reports of a certain virus has increased eponentiall since The current number of cases can be approimated using the function r(t) = 07 e 0.00t, where t is the number of ears since Estimate the of cases in the ear 0. A) 190 B) 66 C) 0 D) 07 16) An initial investment of $1,000 is invested for ears in an account that earns % interest, compounded quarterl. Find the amount of mone in the account at the end of the period. A) $1,99.8 B) $99.8 C) $1,86.6 D) $1,979.0 Answer: A 17) Suppose that $00 is invested at 3% interest, compounded semiannuall. Find the function for the amount of mone after t ears. A) A = 00 (1.03) t B) A = 00 (1.01) t C) A = 00 (1.01) t D) A = 00 (1.01) t 73

74 Use the REGRESSION feature on a graphing calculator. 18) A strain of E-coli Beu-recA1 is placed into a petri dish at 30 Celsius and allowed to grow. The following data are collected. Theor states that the number of bacteria in the petri dish will initiall grow according to the law of uninhibited growth. The population is measured using an optical device in which the amount of light that passes through the petri dish is measured. Time in hours, Population, Find the eponential equation in the form = a b, where is the hours of growth. Round to four decimal places. A) = B) = C) = D) = ) The total cost of the Democratic and the Republican national conventions has increased 96% over the 0-ear period between 1980 and 00. The following table lists the total cost, in millions of dollars, for selected ears. Year, Cost, 1980, = 0 $ , = , = , = , = , = , = 170. Find the eponential functions that best estimates this data. Round our answer to four decimal places A) = (.887) B) = C) =.887 (1.099) D) =.887 (1.099) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. ) A particular bacterium is found to have a doubling time of 0 minutes. If a laborator culture begins with a population of 300 of this bacteria and there is no change in the growth rate, how man bacteria will be present in minutes? Use si decimal places in the interim calculation for the growth rate. Answer:,018 bacteria 7

75 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert to a logarithmic equation. 11) 3 = 8 A) log 3 = 8 B) log 8 = 3 C) log 3 8 = D) log 8 = 3 1) = A) = log B) = log C) = log D) = log Answer: A 13) = 3 A) = log 3 B) 3 = log C) = log D) = log 9 Answer: A 1) e t = 7 A) ln t = 7 B) ln 7 = t C) log 7 t = e D) log 7 e = t Answer: A Convert to an eponential equation. 1) log 9 7 = 3 A) 3 = 9 7 B) 9 = 7 3/ C) 7 = 9 3/ D) 7 = 3 9 7

76 Evaluate. 16) log 8 1 = t A) 8 1 = t B) 8 t = 1 C) t 8 = 1 D) 1 8 = t 17) ln = 3.78 A) e 3.78 = ln B) e 3.78 = C) e = 3.78 D) e 3.78 = 1 18) log 8 8 A) 8 B) 8 C) D) 3 Use a calculator to evaluate the epression. Round the result to five decimal places. 19) log 0.17 A) B) C) D) ) log 0.3 A) B) C) 0.3 D) ) log 1.37 A) B) C) 1.37 D) Undefined 76

77 16) log (-.) A) B).378 C) 1.07 D) Undefined Answer: D 163) log A) B) C) D) ) ln 0.07 A) B) C) D) Undefined 16) ln 97 A) B).6977 C) D) Answer: D Write in terms of simpler forms. 166) log XY A) log 1 X + log 1 Y B) log X + log Y C) log X - log Y D) log 1 X - log 1 Y 167) log b A) log b + log b B) log b - C) log b D) log b - log b Answer: D 77

78 168) logb M 9 A) M + logb 9 B) M logb 9 C) 9 + logb M D) 9 logb M Answer: D 169) a log b A) a b B) b a C) a b D) b a Answer: D Solve for to two decimal places (using a calculator). 170) 700 = 00(1.0) A) 1.3 B) 0 C) 1.0 D) 8.8 Answer: D 171). = A).17 B).97 C) 1.07 D).3 Use the properties of logarithms to solve. 17) log 7 + log 7 ( - ) = log 7 A) 6 B) C) 7 D) Answer: A 173) log b - log b = log b - log b ( - 3) A), B) C) 3 D) Answer: D 78

79 17) log b ( + 3) + log b = log b A) 6 B) 3 C) -6, -3 D) -6 Answer: A 17) log 6 ( - ) = 1 A) 11 6 B) log C) 7 D) 11 Answer: D 176) ln (3 - ) = ln 0 - ln ( - ) A) 0, 19 3 B), 3 C) 19 3 D) -, ) log ( + ) - log ( + ) = log A) - B) C), - D) 6 178) log ( - 9) = 1 - log A) -1, B) -, 1 C) D) - Graph b converting to eponential form first. 79

80 179) = log ( - 1) A) B) C)

81 D) Answer: D 180) = log ( + 3) A)

82 B) C) D) Answer: D Graph the function using a calculator and point-b-point plotting. Indicate increasing and decreasing intervals. 8

83 181) f() = 3 ln - - A) Increasing: (-3, ) - - B) Increasing: (0, ) - - C) Decreasing: (0, )

84 D) Decreasing: (0, ) ) f() = - ln - - A) Decreasing: 0, 1 Increasing: 1, - - 8

85 B) Decreasing: (0, -] Increasing: [-, ) - - C) Decreasing: (0, ) - - D) Decreasing: (0, 1] Increasing: [1, ) - - Answer: D 8

86 183) f() = -3 - ln - - A) Decreasing: (0, ) - - B) Increasing (0, ) - - C) Decreasing: (0, )

87 D) Increasing (-3, ) ) f() = - ln( + ) A) Decreasing: (-, )

88 B) Decreasing: (-, ) C) Decreasing: (0, ) D) Decreasing: (, ) Solve the problem. 18) If $ is invested at a rate of 8 1 % compounded monthl, what is the balance after ears? [A = P(1 + i) n ] A) $31. B) $19.31 C) $81. D) $8.31 Answer: D 88

89 186) If $,000 is invested at 7% compounded annuall, how long will it take for it to grow to $6,000, assuming no withdrawals are made? Compute answer to the net higher ear if not eact. [A = P(1 + r) t ] A) ears B) 8 ears C) ears D) 6 ears Answer: D 187) In North America, cootes are one of the few species with an epanding range. The future population of cootes in a region of Mississippi valle can be modeled b the equation P = ln(18t + 1), where t is time in ears. Use the equation to determine when the population will reach 170. (Round our answer to the nearest tenth ear.) A) 83.1 ears B) 86. ears C) 78.0 ears D) 81.3 ears 188) A countr has a population growth rate of.% compounded continuousl. At this rate, how long will it take for the population of the countr to double? Round our answer to the nearest tenth. A).9 ears B) 30 ears C).9 ears D) 8.9 ears Answer: D 189) A carbon-1 dating test is performed on a fossil bone, and analsis finds that 1.% of the original amount of carbon-1 is still present in the bone. Estimate the age of the fossil bone. (Recall that carbon-1 decas according to the equation A = A0e t ). A) 1, 000 ears B) ears C) 1,03 ears D) 1,00 ears 190) Assume that a savings account earns interest at the rate of % compounded monthl. If this account contains $00 now, how man months will it take for this amount to double if no withdrawals are made? A) 1 months B) 17 months C) 0 months D) 08 months 89

90 191) U. S. Census Bureau data shows that the number of families in the United States (in millions) in ear is given b h() = log, where = 0 is How man families were there in 00? A) 1 million B) 90 million C) 7 million D) 8 million 19) The level of a sound in decibels (db) is determined b the formula N = log(i 1 ) db, where I is the intensit of the sound in watts per square meter. A certain noise has an intensit of watts per square meter. What is the sound level of this noise? (Round our answer to the nearest decibel.) A) 89 db B) 06 db C) 79 db D) 9 db Answer: A 193) Book sales on the Internet (in billions of dollars) in ear are approimated b f() = ln, where = 0 corresponds to 000. How much will be spent on Internet book sales in 008? Round to the nearest tenth. A) 6. billion B) 6.0 billion C) 3.9 billion D) 8.0 billion Answer: A 90