Semester 1 Exam Review

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1 Semester 1 Exam Review Name Show all your work on a separate sheet this will be turned in the day of the exam and count towards calculation of your semester exam grade. Chapter 1 1. Solve. x 6 5 x 6 x 6 A) No solution B) 6 C) 6 D). Solve for x. x y x 4 4 y A) x B) y 1 1 x C) y 1 1 x D) y 1 4 y x y 1. For what real numbers x does the expression represent a real number? x + 6 A) x 6 B) All real numbers except x = 6 C) x 6 D) x > 6 4. A musician is planning to market a CD. The fixed costs are $560 and the variable costs are $5 per CD. The wholesale price of the CD will be $9. For the artist to make a profit, revenues must be greater than costs. How many CDs, x, must be sold for the musician to make a profit? A) x > 150 B) x > 160 C) x > 140 D) x > Solve. Write the solution in interval notation. x + 4 A) [ 7, 1] B) ( 7, 1) C) (, 7) (1, ) D) (, 7] [1, ) 6. Solve. x = x 11 A) 1 i 10 B) 1 i 4 C) 1 i 4 D) 1 i When a stone is dropped into a deep well, the number of seconds until the sound of a x x splash is heard is given by the formula t, where x is the depth of the well 4 1,50 in feet. For one particular well, the splash is heard 10 seconds after the stone is released. How deep (to the nearest foot) is the well? A) 1,450 ft B),75 ft C) 1,50 ft D) 1,06 ft Copyright 011, McGraw Hill, Barnett Page 1

2 Chapter 8. Find the equation of the line with slope 4 and y-intercept 7. Write the equation in standard form Ax + By = C, A 0. A) 4x + y = 7 B) 4x y = 7 C) 4x y = 7 D) 4x + y = 7 9. Write the equation of the line passing through ( 5, 4) and ( 5, 6). A) y = 5 B) y = x C) x = 5 D) y = x Write the equation of the line which passes through (, 1) and is perpendicular to the line with equation y x = 1. A) x y = 5 B) x + y = 1 C) x + y = 5 D) x y = 7 Use the following to answer questions 11-1: The Number Two Plumbing Co. charges $40 per hour plus a fixed service call charge of $ Write an equation that will allow you to compute the total bill for any number of hours, x, that it takes to complete a job. A) 40x + 55C = 0 B) 55x + 40C = 0 C) C = 40x + 55 D) C = 55x If the bill comes to $145.00, how many hours did the job take? A).15 hours B).5 hours C).45 hours D) 1.95 hours Use the following to answer questions 1-15: A business purchases a copier for $4,500 and anticipates it will be worth $1,500 after 10 years. 1. Use straight-line depreciation to find a linear model for the depreciated value V of the copy machine after t years of use. A) V = ,500 t C) V = 4,500 00t B) V = 4, t D) V = 00 4,500 t 14. Interpret the slope of the linear model for the depreciated value of the copy machine. A) The copier's original value was $4,500. B) The copier's original value was $00. C) The copier's value is decreasing by $00 per year. D) The copier's value is decreasing by $4,500 per year. 15. What is the copier's value after 5 years of use? A) $,100 B) $,050 C) $,950 D) $,000

3 Use the following to answer questions 16-17: x + y = Graph the line. A) C) (Gridlines represent one unit each) (Gridlines represent one unit each) B) D) (Gridlines represent one unit each) (Gridlines represent one unit each) 17. Indicate the slope. A) B) C) D) 18. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. Sketch the graph of the equation. xy 5 A) Symmetric with respect to the origin. C) Symmetric with respect to the y-axis. B) Symmetric with respect to the x-axis. D) Symmetric with respect to the origin. Chapter 19. Indicate whether the graph is the graph of a function. A) Not a function B) Function

4 0. Determine whether the correspondence defines a function. Let F be the set of all faculty teaching Physics 101 at a university, and let S be the set of all students taking that course. Students from set S correspond to their Physics 101 instructors. A) Not a function B) A function 1. Find the domain of the function. Express your answer in interval notation. f x x A), B),, 5 5 C), 5 D), 5. If f (x) = x + x, find and simplify f x h f x h. A) x + x + C) x + xh + B) x + x + h + D) x + xh + h +. The area of a rectangle is 58 square inches. Express the perimeter P as a function of the width w. A) P(w) = w + 116w C) P(w) = B) P(w) = w + 58w D) P(w) = 4. Determine whether the function is even, odd, or neither. f (x) = x 5x A) Odd B) Neither C) Even 58 w w 116 w w 5. Solve the inequality. x + x 56 0 A) (, 7] [8, ) B) [ 7, 8] C) (, 8] [7, ) D) [ 8, 7] Use the following to answer questions 6-8: 5 x + 5 f x x Find the domain of f. A) {x x 4} B) {x x 5, 4} C) All real numbers D) {x x 5} 7. Find the x-intercept. A) 5 B) 5 C) None D) Find the y-intercept. A) None B) 5 C) 5 D) 5 8

5 10 if x f x x1 if x4 4 if x 4 Evaluate f ( 7). A) 6 B) 7 C) 4 D) Solve the inequality. x < 11 A) 11, 11 B), 11 11, C) 11 D) No solution 1. The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g. The graph of f ( x) x is horizontally stretched by a factor of 0., reflected in the y axis, and shifted three units to the left. A) gx ( ) ( x ) C) gx ( ) ( x ) B) gx ( ) ( x ) D) g( x) ( x ). Find the vertex form of the quadratic function f (x) = x 1x 1. A) f (x) = (x + 6) 5 C) f (x) = (x + 6) + 5 B) f (x) = (x 6) 5 D) f (x) = (x 6) + 5 Use the following to answer questions -4: f x x and gx x 1. Find (g f)( ). A) Undefined B) 0 C) D) 4. Find (g f)(1). Use the following to answer questions 5-6: 4 f (x) = and g(x) = x x 5 5. Find f / g. A) f x15 f x C) x g 4x8 g 4 x x 5 B) f x 5 f 4x x D) x g 4x g x 5 6. Determine the domain of f / g. A) (, 5) ( 5, ) (, ) C) (, ) (, ) B) (, ) D) (, 5) ( 5, )

6 7. Determine whether the function is one-to-one. f (x) = x 9 A) Not one-to-one B) One-to-one 8. A music store sells a CD with a wholesale price of $5 for $11.5 and one with a wholesale price of $15.00 for $.75. If the markup policy for the store is assumed to be linear, find a function r = m(w) that expresses the retail price r as a function of the wholesale price w. A) r = m(w) = 5w C) r = m(w) = 5w 1.5 B) r = m(w) = 1.5w 5 D) r = m(w) = 1.5w Find the inverse function f 1. f (x) = 5x + 7 A) 1 1 f x x + 7 C) 5 1 f 1 x x 7 5 B) D) f x x f x x Find the vertex and axis of the parabola, then draw the graph. f( x) ( x) A) Vertex: (, ); axis: x = C) Vertex: (, ); axis: x = B) Vertex: (, ); axis: x = D) Vertex: (, ); axis: x = Chapter 4 Use the following to answer questions 41-4: The graph of the polynomial function P(x) is shown. 41. List the real zeros of P(x). A) 0 B), 0, 1 C) 1 D), 1

7 4. List the turning points of P(x). A) (, 0), (1, 0) B) (, 0) C) (0, 4) D) (, 0), (0, 4) 4. State the left and right behavior of P(x). A) P(x) as x and P(x) as x B) P(x) as x and P(x) as x C) P(x) as x and P(x) as x D) P(x) as x and P(x) as x 44. Use long division to compute the quotient and remainder. ( 4 + x + 5x ) (x + 1) A) 5x, R = B) 5x, R = C) 5x +, R = D) 5x +, R = 45. Determine whether x + 1 is a factor of x 4x 4x + 1. A) No B) Yes 46. A propane gas tank is in the shape of a right circular cylinder with a hemisphere at each end. If the overall length of the tank is 0 feet and the volume is 0π cubic feet, find the common radius of the hemispheres and the cylinder. x x 0 ft A) 1.4 feet B) 1.1 feet C) 1. feet D) 1. feet Use the following to answer questions 47: P(x) = x 4 x x 5x + 4; (, ) 47. Use the Intermediate Value theorem to explain why the polynomial function has a zero in the interval. A) P() > 0 and P() < 0 C) P() < 0 and P() < 0 B) P() < 0 and P() > 0 D) P() > 0 and P() > Solve the inequality. x 4 0x < 64 A) (, 4) (, ) C) ( 4, ) (, 4) B) (, ) (4, ) D) (, 4) (, ) (4, ) 49. Find all other zeros of P(x) = x + x + 4x + 0 given that 1 i is a zero. A) 1 i and B) 1 i and C) 1 + i and D) 1 + i and

8 50. Find the zeros of the polynomial and indicate the multiplicity of each. P(x) = (x 9) 4 (x + 4) (x 5i) A) (multiplicity 4), (multiplicity 4), i (multiplicity ), i (multiplicity ), 5i (multiplicity ) B) (multiplicity 8), (multiplicity 6), 5i (multiplicity ) C) i (multiplicity 4), i (multiplicity 4), (multiplicity ), (multiplicity ), 5i (multiplicity ) D) (multiplicity 4), (multiplicity 4), (multiplicity ), (multiplicity ), 5i (multiplicity ) 5. Find a polynomial P(x) having root i, degree, leading coefficient 1, and real coefficients. Write the polynomial in expanded form. A) P(x) = x 6x + 5 C) P(x) = x + 6x + 5 B) P(x) = x 6x + 1 D) P(x) = x + 6x Find the oblique asymptote if it exists. x 8x9 f x x 6 A) y = x B) y = x + C) No oblique asymptote exists. D) y = x x 5. Solve the inequality. 0 x 1 A) (, ] (1, ) B) (, ] [1, ) C) [, 1] D) [, 1) 54. Find a polynomial of lowest degree, with leading coefficient 1, that has the indicated graph. Assume all zeros are integers. 0 y -5 5 x -0 Use the following to answer questions 55-56: f (x) = 6 x 0 x Complete the statement: As x 5, f (x) A) B) 0 C) D) Complete the statement: As x, f (x) A) 6 B) C) 0 D)

9 57. Translate the following statement into an equation, using k as the constant of variation. x varies directly as y and inversely as z. z ky y kz A) x B) x C) x D) x ky z kz y 58. y varies inversely as the cube root of x. If y = 4 when x = 7, find y when x = 8. A) 16 B) 96 C) 4 D) Graph f x A) x. NO CALCULATOR! x 4 C) B) D) Chapter Evaluate e 6 e 6 to four significant digits. A) B) C) 40.4 D) Find the equations of any horizontal asymptotes without graphing. x y = e + 8 A) y = 8 B) y = 8 C) No horizontal asymptote D) y = 0

10 6. The bacteria in a certain culture double every 7.9 hours. The culture has 4,000 bacteria at the start. How many bacteria will the culture contain after 6 hours? A) 6,871 bacteria B) 6,991 bacteria C) 6,77 bacteria D) 6,669 bacteria 6. The radioactive element americium-41 has a half-life of 4 years. Suppose we start with a 0-g mass of americium-41. How much will be left after 149 years? Compute the answer to three significant digits. A) 18.6 g B) 18.0 g C) 15.7 g D) 16.8 g 64. An employee is hired to assemble toys. The learning curve 00 N 0.t 5 4e gives the number of toys the average employee is able to assemble per day after t days on the job. How many toys can the average employee assemble per day after days of training? Round to the nearest integer. A) 18 toys B) 16 toys C) 19 toys D) 17 toys Use the following to answer questions 65-66: x y c 65. Find a logistic regression model y bx 1 ae for the data. A) 45.9 y x e 11.0 y x e B) 45.9 y x e 11.0 y e 66. Use the model to find the approximate value of y when x = 8. A) 190 B) 150 C) 10 D) 170 x 67. Write in logarithmic form. 81 = 4 A) log 81 = 4 B) log 4 = 81 C) log 81 = 4 D) log 4 = 81

11 68. Simplify. 1 log 5 5 A) B) 1 C) D) Solve. A) 5 4 log 16 = x B) 4 5 C) 1 D) 70. Given that log x and log 5, A) 10,15 B) 06 C) 180 D) 7 4 y find log x y. 71. Graph the logarithmic function. f (x) = log (x 1) A) C) B) D) 7. Find f 1 if f (x) = log 6 (x ). A) f 1 (x) = 6 x/ + C) f 1 (x) = 6 x B) f 1 (x) = 6 x/ D) f 1 (x) = 6 x + 7. A radio is playing at a volume with an intensity of I = W/m. Find its rating in decibels to two significant digits. 10log A) 5 db B) 76 db C) 67 db D) 60 db

12 74. A solution has a hydrogen ion concentration of [H + ] = Find the ph of the solution. Round your answer to one decimal place. ph = -log[h + ] A) 7.6 B) 7.7 C) 7.8 D) 7.5 The following table shows the number of pounds a person lost since beginning a diet. Use it to answer questions Time (days) Pounds Lost Find a logarithmic regression model for the data. A) y = ln x C) y = ln x B) y = ln x D) y = ln x 76. According to the regression model, what is the projected weight loss for 65 days? A). pounds B).7 pounds C) 8.8 pounds D) 1.1 pounds 77. Solve exactly. log(x 5) = A) 5 B) 4 C) 5 D) Solve. Round your answer to three decimal places. e.7x + 7 = 0 A) No solution B) 19.7 C) D) How many years will it take $6,500 to grow to $7,169 if it is invested at an annual rate of.5%, compounded continuously? Round your answer to one decimal place. A). years B). years C) 1.8 years D).8 years 80. A mathematical model for population growth is given by P = P 0 e rt where P is the population after t years, P 0 is the population at t = 0, and the population is assumed to grow continuously at the annual rate r. How long would it take a population to triple if the growth rate were 4.6%? Round to one decimal place. A) 5.4 years B).9 years C) 4.4 years D) 4.9 years