Math 1324 Final Exam Review Questions

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the equation.1) 42s + 10 = 7s 1)

2) (y - 5) - (y + 2) = 6y 2)

3) 15

(r + 6) = 17

(r + 8) 3)

Find the zero of f.4) f(x) = 3x + 6 4)

You are given a table showing input and output values for a given function y1 = f(x). Use the table to answer thequestion.

5) What is the x-intercept of the graph of y = f(x)? 5)

Two linear functions, y1 and y2 are graphed in a viewing window with the point of intersection of the graphs given in thedisplay at the bottom. Use the intersection method to solve the equation y1 = y2.

6) 6)

Solve the formula for the specified variable.

7) F = 95

C + 32 for C 7)

Solve the equation for y.8) 3x - 10y = -6 8)

1

Solve the problem.9) A repair company's charge for repairing a certain type of copy machine fits the model

y = 47.38 + 0.617x where y is the number of dollars charged and x is the number of minutesthe repair person is on the job. How many minutes would it take for the cost of repair toreach $70? (Round to the nearest minute.)

9)

Use the data shown in the scatter plot to determine whether the data should be modeled by a linear function.10) 10)

Create a scatter plot for the set of data. Use the scatter plot to determine whether the data can be fit exactly to a linearfunction, can be fit only approximately to a linear function, or cannot be fit to a linear function.

11) x 1 2 3 4 5y 9 11 12 15 17

11)

Write the best-fit linear model for the data.12) Two different tests are designed to measure employee productivity and dexterity. Several

employees are randomly selected and tested with these results. Find the linear function tomodel this data.

ProductivityDexterity

23 25 28 21 21 25 26 30 34 3649 53 59 42 47 53 55 63 67 75

12)

Give the coordinates of the point of intersection of the linear equations.13) 4x + y = -24

2x + 4y = -2613)

Does the system have a unique solution, no solution, or many solutions?14) 6x - y = 32

x + 2y = 1414)

2

Solve the system of equations by substitution, if a solution exists.15) 8x + 9y = 100

6x - 7y = 2015)

Solve the system of equations by elimination, if a solution exists.16) x - 3y = 1

7x - 2y = 716)

To find the number of units that gives break-even for the product, solve the equation R = C. Round your answer to thenearest whole unit.

17) A manufacturer has total revenue given by the function R = 150x and has total cost givenby C = 46,000 + 30x, where x is the number of units produced and sold.

17)

Solve the problem.18) A certain product has supply and demand functions given by p = 7q + 22 and p = 297 - 4q,

respectively, where p is the price in dollars and q is the quantity supplied or demanded atprice p. What price gives market equilibrium?

18)

19) There were 38,000 people at a ballgame in Los Angeles. The day's receipts were $260,000.How many people paid $12 for reserved seats and how many paid $5 for generaladmission?

19)

Determine if the graph of the function is concave up or concave down.20) f(x) = -3x2 - 2x - 8 20)

Determine if the vertex of the graph is a maximum point or a minimum point.21) f(x) = -4x2 - 2x - 7 21)

Provide an appropriate response.22) Write the equation of the quadratic function whose graph is shown. 22)

Solve the problem.23) John owns a hot dog stand. He has found that his profit is given by the equation

P = -x2 + 72x + 79, where x is the number of hot dogs sold. How many hot dogs must hesell to earn the most profit?

23)

3

Use factoring to solve the equation.24) 6y2 + 17y + 12 = 0 24)

Use the square root method to solve the equation.25) 4z2 + 4 = 680 25)

Solve the equation by completing the square.26) p2 + 5p - 5 = 0 26)

Use the quadratic formula to solve the equation.27) z2 + z - 5 = 0 27)

Graph.28) y = x - 2 28)

Graph the function.

29) f(x) =x2 - 4, if x < -10, if -1 x 1x2 + 4, if 1 < x

29)

Find the requested value.30)

f(7) for f(x) =2x + 6 if x 05 - 6x if 0 < x < 6

x if x 6

30)

4

Solve the equation.

31) 13

x - 8 = 4 31)

Solve the problem.

32) A manufacturer's cost is given by C = 4003

n + 200, where C is the cost and n is thenumber of parts produced. Find the cost when 512 parts are produced.

32)

33) If the average cost per unit C(x) to produce x units of plywood is given by C(x) = 300x + 10

,

what is the unit cost for 10 units?

33)

Find a quadratic function that best fits the data. Give answers to the nearest hundredth.

34) x -4 0 7y -8 12 -17

34)

Find a power function that models the data in the table. Round to three decimal places if necessary.

35) x 1 2 3 4 5y 9 14 18 19 23

35)

Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.36) f(x) = 3x3 36)

Determine whether the function is even, odd, or neither.37) f(x) = (x + 1)(x + 9) 37)

For the pair of functions, perform the indicated operation.

38) f(x) = 2x2 - 7x, g(x) = x2 - 4x - 21 Find fg

(x). 38)

Evaluate.

39) If f(x) = 2x + 10 and g(x) = x2 + 3, evaluate gf

(1). 39)

Find the requested composition of functions.40) Given f(x) = -6x + 9 and g(x) = 3x + 8, find (g f)(x). 40)

Solve the problem.41) The function f(x) = 60x computes the number of minutes in x hours. The function g(x) = 24x

computes the number of hours in x days. What is (f g)(x) and what does it compute?41)

Determine if the function is a growth exponential or a decay exponential.42) y = 8e-9x 42)

5

Graph the function.

43) f(x) = 12

x43)

Find the function value.

44) Let f(x) = 13

x. Find f(2). 44)

Solve the problem.45) The number of books in a small library increases according to the function B = 4500e0.03t,

where t is measured in years. How many books will the library have after 5 years?45)

Write the logarithmic equation in exponential form.46) log5 (25) = 2 46)

Write in logarithmic form.47) 23 = 8 47)

Find the value of the logarithm without using a calculator.48) log 8 32 48)

Graph the function.49) y = log2 x 49)

6

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible.

50) log 7

9m

2n

k250)

Rewrite as a single logarithm.

51) 5 log a q -53

log a r +12

log a f - 6 log a p 51)

Solve the problem.52) The sales of a new product (in items per month) can be approximated by

S(x) = 250 + 200 log(3t + 1), where t represents the number of months after the item firstbecomes available. Find the number of items sold per month 33 months after the item firstbecomes available.

52)

53) The number of periods needed to double an investment when a lump sum is invested at

14%, compounded semiannually, is given by n = ln 2ln 1.07

. Find n, rounded to the nearest

tenth.

53)

Solve the equation. If necessary, round to thousandths.54) 47x = 1024 54)

Solve the problem.55) The sales of a mature product (one which has passed its peak) will decline by the function

S(t)= S0e-at, where t is time in years. Find the sales after 14 years if a = 0.2 and S0 = 62,200.55)

56) Find the exponential function that models the data in the table below.

x f(x)-2 -34-1 -20.40 -12.241 -7.3442 -4.4064

56)

57) Find the logarithmic function that models the data in the table below.

x 1 2 3 4 5y 1.3 4.9 6.8 8.0 9.2

57)

Evaluate.

58) P 1 + rk

kn for P = $480, n = 8, r = 7%, k = 4 58)

Solve the problem.59) Find the amount of money in an account after 6 years if $1800 is deposited at 6% annual

interest compounded semiannually.59)

7

60) Charles wants to retire in 17 years. At that time he wants to be able to withdraw $22,000 atthe end of each year for 20 years. Assume that money can be deposited at 12% per yearcompounded annually. What exact amount will Charles need in 17 years?

60)

Evaluate the function. Round to two decimal places.

61) Evaluate 800(0.02)0.2t for t = 10. 61)

Graph the function.

62) f(x) = 4601 + 10e-0.2x

62)

63) f(x) = 6000(0.002)0.5x 63)

Solve the problem.64) The natural resources of an island limit the growth of the population to a limiting value of

4625. The population of the island is given by the logistic equation P(t) = 46251 + 4.22e-0.32t

,

where t is the number of years after 1980. What is the population of the island in 1987?

64)

65) A company predicts that sales will increase rapidly after a new product is released, with

the number of units sold weekly modeled by N = 5000(0.2)0.5t, where t represents thenumber of weeks after the product is released. How many units per week were sold at theend of the first week of the campaign?

65)

8

Use the given graph of the polynomial function to estimate the x-intercepts.66) 66)

Determine whether the polynomial function is cubic or quartic.67) f(x) = 17x4 - 12 + 0.14x2 - 6x 67)

Approximate the coordinates of each turning point by graphing f(x) in the standard viewing rectangle. Round to thenearest hundredth.

68) y = 125

(x3 - 3x2 - 45x + 5) 68)

Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearesthundredth.

69) y = 3x3 - 4x2 - 6x + 2 69)

Find the cubic or quartic function that models the data in the table.

70) x 3 4 6 8y 10 15 21 33

(Cubic) 70)

71) x 0 3 7 9 11y -1 5 9 15 19

(Quartic) 71)

Solve the polynomial equation.72) (2x + 1)2(9 - x)2 = 0 72)

9

Use the graph of the polynomial function f(x) to solve f(x) = 0.73) 73)

Solve the problem.74) Suppose c(x) = x3 - 24x2 + 10,000x is the cost of manufacturing x items. Find a production

level that will minimize the average cost of making x items.74)

Use synthetic division to find the quotient and remainder.75) (2x4 - x3 - 15x2 + 3x) ÷ (x + 3) 75)

Solve the problem.76) The profit function for a product is given by P(x) = -0.4x3 + 66x2 - 2120x - 48,000 dollars,

where x is the number of units produced and sold. Determine the levels of production andsale that give break-even.

76)

Give the equations of any vertical asymptotes for the graphs of the rational functions.

77) f(x) = x - 5x2 - 36

77)

Give the equations of any horizontal asymptotes for the graphs of the rational functions.

78) h(x) = 7x2 - 2x - 39x2 - 9x + 3

78)

Solve the problem.79) Suppose the cost per ton, y, to build an oil platform of x thousand tons is approximated by

y = 62,500x + 125

. What is the cost per ton for x = 20?

79)

Use analytical and graphical methods to solve the inequality.80) (2x + 5)(x - 9)(3x - 8) 0 80)

81) -7-5x - 4

> 0 81)

10

Use the given feasible region determined by the constraint inequalities to find the maximum possible value of theobjective function.

82) f = 3x + 11y subject to the constraints5x + 4y 180x + 2y 66x 0, y 0

82)

Solve the problem.83) A mechanic is testing the cooling system of a boat engine. He measures the engine's

temperature over time. Use a graphing utility to fit a logistic function to the data. What isthe carrying capacity of the cooling system?time, min 5 10 15 20 25temperature, °F 100 180 270 300 305

83)

11

Answer KeyTestname: FINAL_REVIEW_QUESTIONS

1) - 27

2) -76

3) -14) -25) 6

6) 5 13

7) C = 59

(F - 32)

8) y = 310

x + 35

9) 37 minutes10) Yes, approximately linear11) only approximately12) y = 5.05 + 1.91x13) (-5, -4)14) A unique solution15) x = 8, y = 416) x = 1, y = 017) 383 units18) $19719) 10,000 people paid $12, and 28,000 people paid $520) Concave down21) Maximum22) y = -(x - 4)2 + 723) 36 hot dogs

24) -32

, - 43

25) ±13

26) -5 ± 3 52

27) -1 ± 212

12

Answer KeyTestname: FINAL_REVIEW_QUESTIONS

28)

29)

30) 731) 12, 3632) $340033) $15.0034) y = -0.83x2 + 1.68x + 1235) y = 9.208x0.56536) Origin37) Neither

38) 2x2 - 7xx2 - 4x - 21

39) 13

40) -18x + 3541) (f g)(x) = 1440x; It computes the number of minutes in x days.42) Decay

13

Answer KeyTestname: FINAL_REVIEW_QUESTIONS

43)

44) 19

45) 5228 books46) 52 = 2547) log 2 8 = 3

48) 53

49)

50) 19

log 7 m +12

log 7 n - 2 log 7 k

51) log aq 5 f 1/ 2

r 5/ 3 p6

52) 650 items per month53) 10.2 periods

54) 57

55) 3782 products56) f(x) = -12.24 · 0.6x57) f(x) = 1.39 + 4.86 ln x58) $836.2659) $2566.3760) $164,327.68

14

Answer KeyTestname: FINAL_REVIEW_QUESTIONS

61) 800.0062)

63)

64) 3191 people65) 2236 units66) -3, -1, 0, 267) Quartic68) (-3, 3.44) and (5, -6.8)69) Loc max value 3.63, loc min value -6.0170) y = 0.28x3 - 4.35x2 + 24.97x - 33.4071) y = -0.01x4 + 0.27x3 - 1.94x2 + 5.70x - 1.00

72) -12

, 9

73) -2, 174) 12 items

75) 2x3 - 7x2 + 6x - 15 + 45x + 3

76) 80 or 100 units77) x = 6, x = -6

78) y = 79

79) $431.0380) x -5/2 or 8/3 x 9

15

Answer KeyTestname: FINAL_REVIEW_QUESTIONS

81) x > -45

82) 363

83) y = 314.791 + 7.86e-0.246x

, 315°F

16