1. f(x) = f(x) = 3. y 2-3y p - 4 8p2. Math 0312 EXAM 3 Review Questions. Name. Find all numbers not in the domain of the function.
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1 Name Find all numbers not in the domain of the function. 1. f(x) = 8 x - 5 Find all numbers that are not in the domain of the function. Then give the domain using set notation f(x) = x x + 24 Express the rational expression in lowest terms. 3. y 2-3y - 10 y2-4y - 12 Write the rational expression in lowest terms. (y - 6)(y - 4) 4. (4 - y)(6 + y) Perform the indicated operation and express in lowest terms. 5. 4p - 4 8p2 p 6p - 6 1
2 6. z z + 36 z2 + 16z + 63 z2 + 4z z2-2z x x Assume that the expressions given are denominators of fractions. Find the least common denominator. 8. 7a + 21, a2 + 3a Add or subtract as indicated. Write the answer in lowest terms y2-3y y x 4 y xy 11. 2ab a2 - b2 - b a - b + 4 2
3 Simplify the complex fraction. x x x x Without actually solving the equation, list all possible numbers that would have to be rejected if they appeared as potential solutions x x - 9 = 0 Solve the equation w w - 8 = -41 3w w
4 Graph the rational function. Give the equations of the vertical and horizontal asymptotes. 16. f(x) = 5 x Solve the problem. 17. The speed of a stream is 5 mph. If a boat travels 52 miles downstream in the same time that it takes to travel 26 miles upstream, what is the speed of the boat in still water? 4
5 Suppose the triangles shown are similar, with angle A = angle D, angle B = angle E, and angle C = angle F. Answer the question. 18. E B A 2x - 7 C D 2x + 4 F What is the value of x? Solve the problem. Round your answer, as needed. 19. Doug and Inga can deliver 100 papers in 4 hours. How long would it take them to deliver 95 papers? Solve the problem. 20. Frank can type a report in 2 hours and James takes 5 hours. How long will it take the two of them typing together? 5
6 Find the root if it is a real number Graph the function and give its domain and its range. 23. f(x) = x - 3 Simplify the root. 24. x 10 Solve the problem. 25. The cost of manufacturing clocks is given by c = 121 n + 16, where c is the total cost and n is the number produced. What is the cost when no clocks are produced? Simplify the expression involving rational exponents / /2 Write with radicals. Assume that all variables represent positive real numbers. 28. (3m + n) 5/6 6
7 Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers u 7 u 3 Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. x /4 y x1/2 x 3/10 x 2/5 (x 2 ) -1/2 Solve the problem. 32. In an economics study, three quantities m, p, and q have been found to be related by the equation m = p 1/2 q 1/2. Find m, if p = 9 and q = 36. Multiply using the product rule xy 3 9xy Simplify the radical. Assume that all variables represent positive real numbers x x 4 2x 7
8 Express the radical in simplified form Express the radical in simplified form. Assume that all variables represent positive real numbers a 8 b y 22 8 Simplify the radical. Assume that all variables represent positive real numbers Simplify by first writing the radicals with the same index. Then multiply Find the unknown length in the right triangle. Simplify the answer if necessary. 41. b
9 Find the distance between the pair of points. 42. (-1, -2) and (1, -6) Simplify. Assume that all variables represent positive real numbers x x x x 7-2x 4 x Solve the problem. Give the answer as a simplified radical expression. 47. Find the perimeter of a lot with sides measuring 3 18, 3 50, 5 8, and 2 27 yards. Multiply, then simplify the product. Assume that all variables represent positive real numbers. 48. ( 5x + 6)( 6x + 4) 9
10 Rationalize the denominator. Assume that all variables represent positive real numbers x 3 y5 Simplify. Assume that all variables represent positive real numbers x2 Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero x 8 + x Write the expression in lowest terms. Assume that all variables represent positive real numbers Solve the equation q - 2 = 2 10
11 56. p 2-5p + 16 = p s + 6 = 4 8s 58. 2x x + 1 = 1 Rewrite the expressions with rational exponents as radical expressions, and then solve the equation. 59. (x 2 + 2) 1/2 - (2x + 5) 1/2 = 0 Solve the formula for the indicated variable. S 60. r = 4 for S Write the number as a product of a real number and i. Simplify the radical expression
12 Multiply or divide as indicated Add or subtract as indicated. Write your answer in the form a + bi. 65. (2-4i) + (9 + 2i) Multiply. 66. (8-2i)(7 + 4i) 67. i(5-5i)(6-8i) Write the expression in the form a + bi i 5 + 2i Find the power of i. 69. i 13 Simplify. 70. i 21 12
13 Answer Key Testname: MATH EXAM 3 - REVIEW QUESTIONS 1. 5 Objective: (6.1) Find Numbers Not in Domain 2. -8, -3; {x x -8, -3} Objective: (6.1) Give Domain of Rational Function 3. y - 5 y - 6 Objective: (6.1) Write Rational Expression in Lowest Terms y 6 + y Objective: (6.1) Write Rational Exprn in Lowest Terms (Recognize Factor of -1) 5. 16p 3 Objective: (6.1) Multiply or Divide Rational Expressions I 6. z - 9 z 7. Objective: (6.1) Multiply or Divide Rational Expressions I 10 17x Objective: (6.2) Add or Subtract Rational Expressions (Common Denom) 8. 7a(a + 3) Objective: (6.2) Find Least Common Denominator x 10y - 11 (y - 1)(y + 1)(y - 2) Objective: (6.2) Add or Subtract Rational Expressions I 1-44x 3 y 12x 4 y 2 Objective: (6.2) Add or Subtract Rational Expressions I 4a + 5b a + b Objective: (6.2) ^Add or Subtract Rational Expressions II x(x + 4) 56 Objective: (6.3) Simplify Complex Fraction Objective: (6.3) Simplify Complex Fraction , 9 Objective: (6.4) List Impossible Values for Solutions 15. Objective: (6.4) Solve Rational Equation 16. x = 0; y = 0 Objective: (6.4) Graph Rational Function and Give Eqn of Vertical Asymptote mph Objective: (6.5) Solve Apps: Distance, Rate, and Time Objective: (6.5) Solve Apps: Geometry hours Objective: (6.5) Solve Apps: Proportions hr Objective: (6.5) Solve Apps: Work Objective: (7.1) Find Square Root Objective: (7.1) Find Higher Roots 1
14 Answer Key Testname: MATH EXAM 3 - REVIEW QUESTIONS 23. [3, ); [0, ) x 2 Objective: (7.3) Use Quotient Rule for Radicals to Simplify Expression 35. 2x Objective: (7.3) Use Quotient Rule for Radicals to Simplify Expression Objective: (7.3) Express Radical in Simplified Form I 24. x 5 Objective: (7.1) Graph Radical Function; Give Domain and Range Objective: (7.1) Simplify Root Objective: (7.1) Solve Apps: Equations with Radical Expressions Objective: (7.2) Simplify Expression Involving Rational Exponent I Objective: (7.2) Simplify Expression Involving Rational Exponent II (3m + n) 5 Objective: (7.2) Write Exponential Expression with Radicals u 16 Objective: (7.2) Simplify Radical Expression II 30. xy 2 Objective: (7.2) Use Rules of Exponents to Simplify Expression I 31. x 11/5 Objective: (7.2) Use Rules of Exponents to Simplify Expression II Objective: (7.2) Solve Apps: Rational Exponents x 2 y 2 Objective: (7.3) Use Product Rule for Radicals to Simplify Expression a 2 b 3 a 2 b 2 Objective: (7.3) Express Radical in Simplified Form II 38. y7 3 y 2 Objective: (7.3) Express Radical in Simplified Form II Objective: (7.3) Simplify Radical by Using Smaller Index Objective: (7.3) Multiply Radicals with Different Indexes Objective: (7.3) Find Unknown Length in Right Triangle Objective: (7.3) Find Distance Between Pair of Points Objective: (7.4) Simplify Sum or Difference of Radicals (Index = 2) x Objective: (7.4) Simplify Sum or Difference of Radicals (Index = 2) 45. 9x 4 x 3 Objective: (7.4) Simplify Sum or Difference of Radicals (Index > 2) Objective: (7.4) Simplify Sum or Difference of Radicals (Fractions) yards Objective: (7.4) Solve Apps: Geometry 48. x x + 6 6x + 24 Objective: (7.5) Multiply and Simplify Radical Expressions
15 Answer Key Testname: MATH EXAM 3 - REVIEW QUESTIONS Objective: (7.5) Rationalize Denominator (Index = 2) 3x 5xy y 3 Objective: (7.5) Rationalize Denominator (Index = 2) 3 15x 3x Objective: (7.5) Rationalize Denominator (Index > 2) Objective: (7.5) Rationalize Binomial Denominator 53. 3x 8 + x 8 + x Objective: (7.5) Rationalize Binomial Denominator Objective: (7.5) Write Radical Expression in Lowest Terms 55. {2} Objective: (7.6) Solve Radical Equation Using Power Rule 56. {5} Objective: (7.6) Solve Radical Equation by Squaring Binomial Objective: (7.6) Solve Radical Equation Using Power Rule (Index > 2) 58. {3, -1} Objective: (7.6) Solve Radical Equation Using Power Rule Twice 59. {3, -1} Objective: (7.6) Solve Eqn with Rational Exponents for Indicated Variable 60. S = 4 r 2 Objective: (7.6) Use Power Rule to Solve Formula for Indicated Variable 61. 2i Objective: (7.7) Write Radical as Product of Real Number and i i 2 Objective: (7.7) Write Radical as Product of Real Number and i Objective: (7.7) Multiply or Divide Radicals Objective: (7.7) Multiply or Divide Radicals i Objective: (7.7) Add or Subtract Complex Numbers i Objective: (7.7) Multiply Complex Numbers i Objective: (7.7) Multiply Complex Numbers i Objective: (7.7) Divide Complex Numbers 69. i Objective: (7.7) Find Power of i 70. i Objective: (7.8) Chapter Test
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