advertisement

Poudre School District’s College Algebra Course Review 1. Perform the indicated operations and simplify the result. Leave the answer in factored form. 9x 9 2 6. Algebraically determine the equation of the line in the form y mx b . 3x 3 22 7. Determine the equation of the line perpendicular to the line you found in #6 that passes through the point ( 3, 7) . a. 33 1 33 11 9x 9 c. 3x 3 33 d. x 1 b. e. 2. Solve: a. b. c. d. e. 8. Determine the equation of the circle with endpoints of a diameter at the given points (8, 2) and ( 4,4) . 9. Find the equation of the line that connects the centers of the two given circles. circle #1: x 2 y 2 6x 12y 1 0 none of the above 2x 3 7x 2 15x 0 . x 1.5, 5 x 0, 1.5, 5 x 5,0,1.5 x 1.5,0,5 circle #2: x 2 none of the above 3. Find the quotient and the remainder of 8x 3 22x 2 7x 13 divided by 2x 3 . 4. Solve: y 2 1 5y 3 4 y For #6-8, consider the two points (8, 2) and ( 4,4) . 2 1 y 2 5. Which expression below is written in a bi form? 1 a. 2i 5 1 b. 2i 5 c. 3 2i d. 3 2i e. none of the above y 2 14x 8y 3 0 For #10-18, use the given graph of the function f to answer the following questions. 1 3y 4 4 7i 2 i 10. 11. 12. 13. 14. Find the domain of f (x) . Find the range of f (x) . List the x-intercept(s). Identify the y-intercept. Find f ( 1) . 15. Is f 5 positive or negative? 2 16. State the interval for which f (x) is negative. 2? 17. For what value(s) of x is f (x) 18. f (x) is increasing on what interval? Poudre School District’s College Algebra Course Review For #19-21, let f ( x ) x 2 19. Evaluate f (3) . 20. Find f (x h) h 5x 3 . f (x) and C and simplify. 21. Solve f ( x ) 3. 22. Algebraically determine whether the following function is even, odd, or neither. h( x ) x3 2 x2 5 23. Given f (x) 2x 2 3x determine the average rate of change from 1 to x. Give answer in simplified factored form. 24. Graph the following piecewise defined function. g ( x) x 2 1 if x 1 3 if 0 x 1 x if x 26. List the sequence of transformations applied to the parent function. 27. Sketch a graph of f (x) with at least 3 points plotted. 28. State the domain and range of f (x) . 29. Solve the system. y z 1 4 x 3y 2z 16 2x 2y 3z 5 30. Solve for x, 3 x 5 9 4 3 6 , B 8 2 0 8 7 1 1 2 3 1 2 y , 4 . Find AB+C. 32. Find the inverse of the following matrix: 3 2 5 7 . For #33-35 assume an 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highway driving and a family’s 300 mile trip required 15.5 gallons of gasoline. 33. Identify the variables in the situation. 34. Write a system of equations based on the situation. 35. Solve the system to find how many whole miles were driven in the city? 0 2 x 5 3. For #25-28, let f ( x ) 25. State the parent function to which transformations are applied. x 31. Let A 8 36. Use the Corner Point principle to maximize z 2x 5y subject to the following constraints. x 0 y 0 x 2y 6 9x 3y 27 a. z 13.8 b. z 12 c. z 14.6 d. z 15 e. None of the above Poudre School District’s College Algebra Course Review 37. Perform each row operation in order, (1) followed by (2) followed by (3), on the given augmented matrix. 1 2 4 3 4 5 10 13 18 13 19 For #39-41, solutions must show appropriate algebraic methods. Let f (x) 2x 2 5x 2 . 39. Find the x-intercept(s). 5 40. Find the y-intercept. 41. Find the vertex of f(x). (1)R2 3R1 R2 (2)R3 (3)R3 4R1 R3 2R2 R3 42. Is the vertex of f(x) a maximum or minimum? Explain how you know using complete sentences. 43. Which of the equations below describes the graph shown? 1 2 a. b. c. d. 4 5 0 1 1 3 0 0 1 5 1 2 4 5 0 1 1 3 0 0 1 5 1 2 4 5 0 1 1 3 0 0 1 5 1 2 4 5 0 1 0 0 1 3 1 5 e. None of the above 38. Find the quadratic function in the form y a(x h) 2 k that has a maximum point at (-1, -17) and passes through (7, 1) a. y b. y 2(x 1) 2 17 1 (x 1)2 17 4 (x 7)2 1 (x 1)2 17 c. y d. y e. None of the above a. f (x) b. f (x) c. f (x) d. f (x) e. 1 4 1 4 1 4 1 4 x 2 2 x 3 x 2 2 x 3 x 2 x 3 2 x 2 x 3 2 None of the above 44. Sketch the given function using the intercepts and end behavior. f ( x) 3x( x 2)2 x 4 For #45-48 let f ( x ) 3 2 x 2 14 x 24 . x 2 2 x 24 45. State the domain of f(x) 46. Find the x-intercept(s) and y-intercept of f(x). Poudre School District’s College Algebra Course Review 47. Find all asymptotes and/or holes. 48. Graph f(x). Be sure to plot at least three points and show all asymptotes. 49. One solution of x 3 5x 2 5x 1 0 is 1. Find the two other solutions. a. 2 3, 2 3 b. 4 3,4 3 c. 2 2 3,2 2 3 d. 4 2 3,4 2 3 e. 51. Find all the zeros of the function. 52. Write the polynomial as a product of linear factors. 53. Use the given zero to find the all remaining complex zeros of the given function. 29 x 3 111 x 2 179 x 78 Given: 3 + 2i is a zero. 54. Find the indicated composite f g x for the pair of functions f ( x) x 9 and g ( x) 8x 13 . a. 2 2 x 1 b. 8 x 9 13 c. 8 x 4 d. 2 2 x 1 e. None of the above 55. Find the inverse function of f ( x) b. f 1 ( x) c. f 1 ( x) d. f 1 ( x) 5x 3 x 3x 3x x 5x 3 2 x 5 2 2 5 2 x 56. Given the graph of f ( x ) 3 x 2 4 , identify the graph below that shows the graph of f 1 . (Note the x and y scale is 2) None of the above 3x 4 f 1 ( x) e. None of the above For #50-52 let y 3x 4 4 x 3 4x 2 4 x 1. 50. Determine the left and right hand behavior of the graph of y . h( x ) a. 3x 2 . (choices above) x 5 Poudre School District’s College Algebra Course Review 57. Use the properties of logarithms to find the exact value of the expression log 5 100 (log 5 8 log 5 2) . a. b. c. d. e. -2 2 4 -4 None of the above 58. Write 3 log 4 (2) 1 log 4 ( x 4) 1 log 4 ( x) 3 2 as a single logarithm with a coefficient of 1. 62. Determine how long it takes a $3000 investment to double if it is invested at 8% compounded semiannually. a. b. c. d. e. 9.2 years 9 years 8.8 years 8.6 years None of the above 63. Solve the equation e 2x 3 11 for x . Round your answers to three decimal places. 64. Solve the equation log( x 3) log x 1 for x . Check 59. If 3 4x 2 what does 812 x equal? 60. An initial deposit of $3,000 is made in a savings account for which the interest is compounded continuously. The balance will double in seven years. What is the annual rate of interest for this account? a. b. c. d. e. 4.3% 6.2% 8.1% 9.9% None of the above 61. The half-life of silicon-32 is 710 years. If a sample presently contains 50 grams, which expression determines how much silicon-32 material will remain after 1650 years? ln(0.5) 710 ln(0.5) b. 50e1650k where k 1650 ln( 0.5) c. 1650e k where k 710 ln(0.5) d. 710e1650k where k 50 a. 50e1650k where k e. None of the above for extraneous solutions. 65. Write the partial fraction decomposition of the rational expression. 5 x 4 5 x 3 18 x 2 11x 11 ( x 1)( x 2 2) 2