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1 FINAL REVIEW WORKSHEET COLLEGE ALGEBRA Chapter Given the following equations, which are functions? (A) y 2 = 1 x 2 (B) y = 9 (C) y = x 3 5x (D) 5x + 2y = 10 (E) y = ± 1 2x (F) y = 3 x + 5 a. all of the above b. none of the above c. B, C, D, and F d. C, D, F e. C only f. C and F 2. Given f(x) = x2 1, find f( 3). x+4 a. 10 b. 10 c. 8 d. 8 e Given f(x) = x2 +3 x 5, find f(1 4 ) 49 a. b. 49 c d What is the domain of this function: f(x) = x 2 x 2 a. (, 1] [2, ) b. (, 2] [1, ) c. ( 2, 1) d. [ 1, 2] 5. What is the domain of this function: f(x) = 3 x x+5 a. (, 5) (3, ) b. x 5, x 3 c. x 5 d. ( 5, 3) 6. What is the range of this function: y = x 2 5 a. (, ) b. [5, ) c. [ 5, ) d. (, 5] 1

2 2 Figure 1 7. Determine which of the following graphs in Figure (1) is the graph of a function. a. A only b. B only c. B and D d. all of these are fuctions e. none of these are functions 8. Find the x- and y- intercepts of 4x 5y + 20 = 0. a. y = 12 b. y = 12 c. y = 3 8 d. y = Given the line 2y = 3x 6, what is the slope and y-intercept? a. m = 3, y int. = 6 b. m = 3, y int. = 2 c. m = 3, y int. = 6 d. m = 3, y int. = 3 2 2

3 10. Find the equation of the line perpendicular to x 2y + 5 = 0 passing through (0, 4). a. y = 1 2 (x 5) b. y = 2x + 4 c. y = 1 2 x d. y = 2x Find the equation of a line through the points (3, 2) and ( 3, 6). a. 2x + 3y = 12 b. 3x + 2y = 12 c. 3x + 2y = 4 d. 2x 3y = Find the equation of a line with x-intercept=2 and y-intercept=-1. a. y = 1x 1 b. y = 2x 1 c. y = 1 x 1 d. y = 2x Given the line: 3x + 2y = 7, which of the following line is perpendicular to this line. a. y = 3 2 x + 4 b. y = 2 3 x 4 c. y = 2 3 x + 3 d. y = 2 3 x Find the equation of a line through the point (2, 1) and parallel to the line 5x 2y = 7. a. 2x 5y = 8 b. 5x 2y = 8 c. 5x + 2y = 4 d. 2x + 5y = 4

4 4 15. Find the rate of change in the following graph: Figure 2 a. \$0.33 per minute b. \$ 0.33 per minute c. \$1.00 per minute d. \$ 3.00 per minute 16. The paired data below consists of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Use linear regression to find the function that predicts the number of products sold as a function of the cost of advertising. Cost N umber a. y = 2.79x b. y = 1.42x 26.4 c. y = 1.42x d. y = 2.79x

5 17. Establish where the following function in Figure (3) is increasing, decreasing, or constant. 5 a. Increasing on (, 0), decreasing on (0, ) b. Increasing on (0, ), decreasing on (, 0) c. Increasing on (, 3), decreasing on (3, ) d. Increasing on (3, ), decreasing on (, 3) 18. Graph the piecewise function f(x) = { 5 x, for x 2 1 3x, for x > 2

6 6 19. For the function f(x) = 3x 2 2x + 5, find f(2x 3) a. 4x 2 12x + 20 b. 12x x + 16 c. 3x d. 12x 2 40x If a graph is symmetric with respect to the y-axis and the point (2, 4) is on the graph, then what point is also on the graph? a. ( 2, 4) b. (3, 4) c. (2, 4) d. ( 2, 4) 21. The graph: x + y = 0 is symmetric with respect to which axis: a. x axis b. y axis c. x axis and y axis d. no symmentries 22. Determine if y = x 3 x is even, odd, or neither even nor odd. a even b odd c neiher 23. The graph of y = x is shifted to the right 4 units and reflected across the x-axis. Write the equation of the new function. a. y = x + 4 b. y = x + 4 c. y = x + 4 d. y = x y varies directly as x 2 and inversely as z; y=4 when x=4 and z=2. Find y when x=2 and z=4. a. y = 2 b. y = 1 2 c. y = 2 d. y = The velocity v of a falling object is directly proportional to the time t of the fall. If, after 2 seconds, the velocity is 64 ft sec. What is the velocity after 5 sec. a ft sec b. 160 ft sec c ft sec d ft sec

7 26. The perimeter of a rectangle is 3 feet. Express its area A as a function of the length x of a side. a. A(x) = x(1 x) b. A(x) = 1.5 x c. A(x) = x(x 3) d. A(x) = x(1.5 x) The volume of a right circular cylinder of height h and radius r is V = πr 2 h. If the height is three times the radius, express the volume V as a function of r. a. V (r) = 3πr 2 h b. V (r) = 3πr 3 c. V (r) = 3πh 3 d. V (r) = 9πh Find the midpoint of a line segment from ( 6, 0) and (2, 4). a. M = ( 2, 2) b. M = ( 3, 4) c. M = 1, 3) d. M = (0, 1) 29. Find the distance between ( 2, 5) and (3, 4). a. d = 26 b. d = 58 c. d = 1 5 d. d = Given the circle with center (2, 5) and radius of 4. What is the equation of the circle. a. x 2 y 2 + 4x 10y = 13 b. x 2 + y 2 + 4x 10y = 13 c. x 2 + y 2 + 4x + 10y = 45 d. x 2 + y 2 4x + 10y = What is the center of circle: x 2 + y 2 + 2x 6y + 9 = 0 a. (1, 3) b. ( 2, 6) c. ( 1, 3) d. (2, 3) Chapter Solve the equation: 1 5 (p + 5) 3 = 1 6 (2p 5) a. p = 7.4 b. p = 8.75 c. p = 9.25 d. p =

8 8 33. Solve for t 2 : S = A r(t 1 t 2 ) a. srt 1 A b. Srt 1 A Sr c. t 1 A d. A Srt 1 Sr 34. Mani pays \$ for a new bike. If the price paid includes a 7.5% sales tax, which is the price of the bike itself? a. \$ b. \$ c. \$ d. \$ Multiply: (4 i) 2 a. 17 4i b i c. 15 8i d. 17 8i 36. Divide: 4 3i 2+5i a i b i c i d Find the value of i 50 a. 1 b. 1 c. i d. i 38. Solve 3x 2 10x + 5 = 0. Simplify your answer. a. 5± 10 3 b. 5± 17 3 c. 10± 10 3 d. 5 ± Solve in the complex number system: x = x 1± a. 11i 1± b. 11 1± c. 17i 3± d. 3i Use a calculator to solve the equation, correct to two decimal places: 2x 2 + x 2 = 0. a. x = 0.78 and x = 1.28 b. x = 1.28 and x = 0.78 c. x = 5.28 and x = 8.92 d. x = 1.78 and x = 3.28

9 9 41. Find the real solutions of the equation: x + 3 x 10 = 0 a. x = 25 b. x = 4 c. x = { 5, 2} d. x = { 4, 4} 42. Solve the following: 3x 2 7x 6 = 0 a. x = { 2, 6} b. x = { 3 2, 1 3 } c. x = { 2 3, 3} d. x = { 2 3, 3} 43. John owns a hotdog stand. He has found that his profit is represented by the equation P (x) = x x + 88, with P being the profit and x the number of hotdogs sold. How many hotdogs must he sell to earn the most profit? a. 38 hotdogs b. 39 hotdogs c. 50 hotdogs d. 25 hotdogs 44. Find the vertex of this parabola: f(x) = x 2 + 2x + 8 a. ( 1, 8) b. (9, 1) c. (2, 8) d. (1, 9) 45. Does the parabola above: a Open up b Open down 46. Find the line of symmetry of the given function y = 2x 2 8x + 4 a. x = 4 b. x = 2 c. x = 4 d. x = 2

10 Match the equation to the correct graph: y = 2(x + 1) Solve the following: 3 x 2 = 1 x (x 1)(x 2) a. no solution b. x = 4 c. x = 3 d. x = Solve the following: 12 x = x a. x = 6 b. x = 6 c. x = 3 d. x = { 3, 4} e. x = { 4, 3} 50. Solve: 3m 1 = 6 a. 7 3 b. 7 3, 7 3 c. 5 3, 7 3 d Solve the inequality: x 8 32 a. [ 56, 72] b. [0, 16] c. [ 72, 56] d. [ 16, 0] 52. Solve the inequality: 32 4x < 32 a. ( 64, 0) b. [ 64, 0] c. [0, 16] d. (0, 16)

11 Chapter Find the polynomial: f(x) = x 2 (x 4), find the x- and y- intercepts of the graph of f. a. y intercept = 0, and x intercept = 0 b. y intercept = 0, and x intercepts = 0, 4 c. y intercept = 0, and x intercept = 4 d. y intercept = 0, and x intercept = 0 e. none of these Given the following functions, which are polynomial function? (A) f(x) = 4x 3 3x 2 (B) f(x) = 1 2 x4 (C) f(x) = x(x 7) (D) f(x) = x 3 + 3x 2 5x 1 (E) f(x) = x2 5 x 4 a. all of the above b. A only c. A and C d. B only e. A and B f. none of the above 55. Use long division to divide 2x 3 + x 2 3x + 2 by x + 3. Give the answer in the form d(x) Q(x) + R(x), where d(x) is the divisor, Q(x) is the quotient and R(x) is the remainder. a. (x + 3) (2x 2 5x + 12) 34 b. (x + 3) (2x 2 5x + 12) + 34 c. (x + 3) (2x 2 5x 12) 34 d. (x + 3) (2x 2 + 7x + 6) Use synthetic division to find f(2), if f(x) = 5x 4 2x 3 + x + 1 a. 35 b. 29 c. 67 d. 95

12 Use synthetic division to find the quotient and remainder for the following problem: (x 3 5) (x 1) a. Q(x) = x 2 + x + 1; R(x) = 4 b. Q(x) = x 2 + x + 1; R(x) = 5 c. Q(x) = x 2 x 1; R(x) = 0 d. Q(x) = x 3 x 2 x 1; R(x) = Use synthetic division to determine if x 3 is a factor of f(x) = 2x 5 4x 4 4x 3 x + 3 a yes b no 59. Find the real solutions of the equation: x 3 2x 2 64x = 0 a. x = { 8, 2, 8} b. x = {2, 8} c. x = { 8, 0, 2, 8} d. x = { 8, 8} 60. Find the zeros of the polynomial function and state the multiplicity of f(x) = 6x 2 (x 9)(x + 3) 3 a. 3 multiplicity 3; 0 multiplicity 2; 3 multiplicity 1; 9 multiplicity 1 b. 3 multiplicity 3; 9 multiplicity 1 c. 3 multiplicity 1; 3 multiplicity 1; 9 multiplicity 1 d. 3 multiplicity 3; 0 multiplicity 2; 9 multiplicity Find a polynomial of degree 3 with 2, 2i, -2i, as zeros a. f(x) = x 3 2x 2 + 4x 8 b. f(x) = x 3 2x 2 4x + 8 c. f(x) = x 3 + 2x 2 + 4ix + 8i d. f(x) = x 3 2ix 2 + 4x Given the polynomial function f(x), find the rational zeros and then the other zeros (that is, solve the equation f(x)=0) f(x) = 3x 4 20x x 2 80x a. { 8, 4, 2i, 2i} b. { 8, 4, i, i} 3 3 c. { 8, 4, 2i, 2i} d. { 4, 4, 4i, 4i} 3 3

13 What kind of asymptotes does this graph have? R(x) = 3x2 +x 4 x 2 4 a. horizontal asymptotes b. horizontal and vertical asymptotes c. horizontal, vertical, and oblique asymptotes d. horizontal and oblique asymptotesno asymptotes 64. Find the horizontal or oblique asymptotes, if any of the graph of R(x) = 36x2 x+8 4x 2 8 a. y = 9 b. x = 9 c. none of these d. y = 9 e. x = Solve: x 2 + 7x 18 > 0 a. (, 9) b. x 9, x 2 c. (, 9) (2, ) d. (, 2) (9, ) 66. Solve: x 6 x+1 3 a. [ 9, ) b. ( 9, 1] c. [ 9, 1) d. (, 9 ] ( 1, ) Chapter For the functions below and (f g)( 2). a. 166 b. 128 c. 156 d. 7 e. 62 f. none of these 68. Given that f(x) = 3x 2 2x + 5 and g(x) = 3x 1, find g f a. 9x 2 6x + 14 b. 9x 3 9x x 5 c. 3x 2 + x + 4 d. 9x 2 + 6x 16

14 Determine which of the following functions are one-to-one. a. A only b. B and C c. D only d. all of the above e. none of the above 70. Find the inverse of f(x) = 2x + 3 a. f 1 (x) = 1(x + 3) b. f 1 (x) = 1 (x 3) 2 2 c. f 1 (x) = 2 x 3 d. f 1 (x) = 2 x+3

15 Match the following functions with the correct graphs. a. y = 2 x b. y = 2 x 1 c. y = 2 (x 1) d. y = 1 2 x 72. Graph the following function y = log 2 x

16 Convert the following to a logarithmic equation e 5 = a. e = log b. ln( ) = 5 c = log 5 e d. ln( 5) = Convert the following to an exponential equation log 10 ( ) = 2 a = 2 b = c. ( )2 = 10 d = Use change of base to find the following: log 5 7 a b c d x 76. Write log 3 x (x+8) 8 factors. as a sum and difference of logarithms. Express all powers as a. log 8 x+ 1 2 log 8(x 2 +4) log 8 (x+8) b. 3 log 8 x+ 1 2 log 8(x 2 +4)+8 log 8 (x+8) c. 3 log 8 x+ 1 2 log 8(x 2 +4) 8 log 8 (x+8) d. 3 log 8 x 1 2 log 8(x 2 +4) 8 log 8 (x+8) 77. Find the value of 3.56 π a b c d Find the domain of this function: y = log(x 2 16) a. ( 16, 16) b. (, 16) (16, ) c. (4, ) d. (, 4) (4, ) e. ( 4, 4) f. none of these 79. Find y such that: log = y a. y = 5 b. y = 5 c. none of these d. y = e. y = 4

17 Solve: 3 log 8 x = log a. x = 36 b. x = 6 c. x = d. x = 6 e. none of these 81. Solve: log 3 (x + 5) log 3 x = 2 a. x = 1 b. x = 5 c. x = 8 5 d. x = Solve: log 2 (x + 3) = 2 log 2 x a. x = 1 b. x = 1 c. x = { 4, 1} d. x = Solve this equation: 75 = 300e 0.24t a. t = b. t = c. t = ln(75) ln(300) d. t = Solve this equation: log 4 (x + 3) + log 4 (2 x) = 1 a. x = { 1, 2} b. x = 2 c. x = 1 d. x = { 2, 1} 85. Solve this equation: 6 x 3 = x a. x = 2 b. x = 11 7 c. x = d. x = Solve this equation: 3 2x + 3 x 2 = 0 a. x = 0 b. x = 1 c. x = { 2, 1} d. x = {2, 1} 87. Solve this equation: 5 x = 3 2x 1 a. x = b. x = c. x = d. x = 1

18 You invest \$25, 000 in an account that is compounded continuously at 5.89% interest for 4 years. Find the value of your investment at the end of those 4 years. a. x = \$15, b. x = \$29, c. x = \$3, d. x = \$31, The population of a city doubled in 12 years. What was the exponential growth rate? a. x = 17.3% b. x = 8.3% c. x = 1.2% d. x = 5.8% Chapter Solve this system of two equations: 2x + 5y = 3 3x 7y = 4 a. x = no solution b. x = 41, y = 17 c. x = 17, y = 41 d. x = 3, y = Solve the following system: 2x y + 3z = 11 x + 3y + z = 10 3x 2y + 4z = 13 a. x = (1, 2, 3) b. x = ( 1, 2, 5) c. x = ( 1, 2, 2) d. (5, 1, 0) 92. Find the equilibrium point for the demand and supply functions D(p) = 85 3p and S(p) = p. a. (\$5, 70) b. (\$7, 49) c. (\$10, 55) d. (\$12, 59)

19 93. To the following matrix perform this row operation: R 2 = 2r 1 + r a b c Let A = ( ) and B = Find AB. a. ( ) b. ( ) c ( ) Find the inverse of the following matrix A = 3 7 ( ) ( ) a. A 1 = 3 2 ( c. A 1 2 = ) b. A 1 = d. A 1 = ( ) d Which of the following represents the graph of 4x 3y 12

20 When a single card is drawn from an ordinary 52-deck, find the probability of getting a Jack? a. b. c. d

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