PreCalculus: Semester 1 Final Exam Review
|
|
- Lesley Williams
- 5 years ago
- Views:
Transcription
1 Name: Class: Date: ID: A PreCalculus: Semester 1 Final Exam Review Short Answer 1. Determine whether the relation represents a function. If it is a function, state the domain and range. 9. Find the domain of the function. f(x) = x Find the domain of the function. h(x) = 2. Determine whether the relation represents a function. If it is a function, state the domain and range. {(19, -4), (3, -3), (3, 0), (12, 3), (28, 5)} 3. Determine whether the equation defines y as a function of x. y = x 4. Determine whether the equation defines y as a function of x. y 2 = 6 - x 2 5. Find the value for the function. Find f(-9) when f(x) = x Find the value for the function. 11. For the given functions f and g, find the requested function and state its domain. f(x) = 4x - 3; g(x) = 8x - 9 Find f - g. 12. For the given functions f and g, find the requested function and state its domain. f(x) = 3x + 4; g(x) = 4x - 6 Find f g. 13. Solve the problem. Find (f + g)(-2) when f(x) = x - 3 and g(x) = x Solve the problem. Find (-3) when f(x) = 3x - 4 and g(x) = 3x x + 3. Find f(4) when f(x) =. 7. Find the value for the function. Find -f(x) when f(x) = 2x 2-3x Find the value for the function. Find f(x - 1) when f(x) = 3x 2-5x
2 Name: ID: A 15. Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. 17. The graph of a function f is given. Use the graph to answer the question. Use the graph of f given below to find f(-6). 16. Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. 18. The graph of a function f is given. Use the graph to answer the question. For what numbers x is f(x) = 0? 19. Answer the question about the given function. Given the function f(x) = -2x 2-4x - 8, is the point (-1, -6) on the graph of f? 2
3 Name: ID: A 20. Answer the question about the given function. Given the function f(x) =, is the point (-2, 8) 23. The graph of a function is given. Decide whether it is even, odd, or neither. on the graph of f? 21. The graph of a function is given. Decide whether it is even, odd, or neither. 24. Determine algebraically whether the function is even, odd, or neither. f(x) = -2x 4 - x The graph of a function is given. Decide whether it is even, odd, or neither. 25. Determine algebraically whether the function is even, odd, or neither. f(x) = -5x Graph the function. f(x) = 3
4 Name: ID: A 27. Graph the function. f(x) = 31. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. f(x) = (x - 7) Match the correct function to the graph. 32. Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. A C 33. Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. A B 29. Write an equation that results in the indicated translation. The absolute value function, shifted 5 units to the left 30. Write an equation that results in the indicated translation. The square root function, shifted 5 units upward 34. Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. (A B) C 35. Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 36. Evaluate the expression using the given values. -3xy + 8y - 5 x = 4, y = 3 4
5 Name: ID: A 37. Evaluate the expression using the given values. x = 7, y = Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. (-4x 2 ) Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. (x 9 y -1 ) Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. (x -6 y 6 ) -7 z Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not Tell whether the expression is a polynomial. If it is, give its degree. 7x Tell whether the expression is a polynomial. If it is, give its degree. 7z 6 + z 44. Add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. 8(1 - y 3 ) + 5(1 + y + y 2 + y 3 ) 45. Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. (2x - 10)(2x + 10) 46. Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in standard form. (x - 10) Find the quotient and the remainder. 9x 8-15x 4 divided by 3x 48. Find the quotient and the remainder. 6x x - 28 divided by x Find the quotient and the remainder. x 4 + 6x divided by x Factor completely. If the polynomial cannot be factored, say it is prime. 9x Factor completely. If the polynomial cannot be factored, say it is prime. 27y Factor completely. If the polynomial cannot be factored, say it is prime. x 2 + 2x + 1 5
6 Name: ID: A 53. Factor completely. If the polynomial cannot be factored, say it is prime. 81x 2-126x Evaluate the expression using the values given in the table. (g f)(1) 54. Factor completely. If the polynomial cannot be factored, say it is prime. 2x 2-2x Factor completely. If the polynomial cannot be factored, say it is prime. 10x x Evaluate the expression using the values given in the table. 56. Use synthetic division to find the quotient and the remainder. x 5 + x 2-4 is divided by x Use synthetic division to find the quotient and the remainder. -3x 3-9x x - 8 is divided by x Use synthetic division to determine whether x - c is a factor of the given polynomial. x 3-4x 2-39x + 126; x Use synthetic division to determine whether x - c is a factor of the given polynomial. x 3-9x 2 + 8x + 64; x Reduce the rational expression to lowest terms. f(g(-5)) 64. For the given functions f and g, find the requested composite function value. f(x) =, g(x) = 5x; Find (f g)(3). 65. For the given functions f and g, find the requested composite function value. f(x) = 4x + 6, g(x) = 4x 2 + 1; Find (g f)(4). 61. Reduce the rational expression to lowest terms. 66. For the given functions f and g, find the requested composite function value. f(x) = 3x + 8, g(x) = ; Find (g f)(3). 6
7 Name: ID: A 67. For the given functions f and g, find the requested composite function. 74. Determine whether the function is one-to-one. f(x) =, g(x) = ; Find (f g)(x). 68. Decide whether the composite functions, f g and g f, are equal to x. f(x) = x 2 + 1, g(x) = Decide whether the composite functions, f g and g f, are equal to x. f(x) =, g(x) = x Indicate whether the function is one-to-one. {(-20, -18), (10, -18), (-8, 18)} 76. Use the horizontal line test to determine whether the function is one-to-one. 70. Find functions f and g so that f g = H. H(x) = 71. Find functions f and g so that f g = H. H(x) = 72. Find the domain of the composite function f g. f(x) = x + 9; g(x) = 77. Use the horizontal line test to determine whether the function is one-to-one. 73. Find the domain of the composite function f g. f(x) = ; g(x) = 7
8 Name: ID: A 78. Find the inverse of the function and state its domain and range. {(-4, -8), (8, 4), (-3, -2), (3, 2)} 79. Graph the function as a solid line or curve and its inverse as a dashed line or curve on the same axes. 2y - 10 = 4x 82. Decide whether or not the functions are inverses of each other. f(x) = (x - 4) 2, x 4; g(x) = The function f is one-to-one. Find its inverse. f(x) = 6x 2-3, x The function f is one-to-one. Find its inverse. f(x) = 85. The function f is one-to-one. State the domain and the range of f and f -1. f(x) = 80. Graph the function as a solid line or curve and its inverse as a dashed line or curve on the same axes. f(x) = 86. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. f(x) = 87. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. f(x) = Form a polynomial whose zeros and degree are given. Zeros: -3, -2, 2; degree Decide whether or not the functions are inverses of each other. f(x) = 3x + 9, g(x) = x Form a polynomial whose zeros and degree are given. Zeros: 0, - 3, 2; degree 3 8
9 Name: ID: A 90. For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. 97. Use the graph to determine the domain and range of the function. f(x) = 4(x - 7)(x - 5) For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. f(x) = 3(x + 2)(x - 4) Find the x- and y-intercepts of f. f(x) = 2x 3 (x - 2) Find the x- and y-intercepts of f. f(x) = (x + 2)(x - 5)(x + 5) 94. Find the domain of the rational function. 98. Graph the function using transformations. f(x) = + 1 G(x) = 95. Find the domain of the rational function. R(x) = 96. Use the graph to determine the domain and range of the function. 9
10 Name: ID: A 99. Graph the function using transformations. f(x) = Graph the function. f(x) = 100. Find the vertical asymptotes of the rational function. f(x) = 105. Graph the function. f(x) = 101. Find the vertical asymptotes of the rational function. f(x) = 102. Give the equation of the horizontal asymptote, if any, of the function. h(x) = 103. Give the equation of the oblique asymptote, if any, of the function. h(x) = 106. Solve the inequality algebraically. Express the solution in interval notation. (x - 5) 2 (x + 7) > Solve the inequality algebraically. Express the solution in interval notation. (x + 2)(x - 2)(x - 7) < 0 10
11 Name: ID: A Essay 108. Analyze the graph of the given function f as follows: (a) Determine the end behavior. (b) Find the x and y intercepts of the graph. (c) Determine whether the graph crosses or touches the x-axis at each x-intercept. (d) Find the domain of f. (f) Use the information obtained in (a) (d) to draw a complete graph of f by hand Analyze the graph of the given function f as follows: (a) Determine the end behavior. (b) Find the x and y intercepts of the graph. (c) Determine whether the graph crosses or touches the x-axis at each x-intercept. (d) Find the domain of f. (f) Use the information obtained in (a) (d) to draw a complete graph of f by hand. 11
12 PreCalculus: Semester 1 Final Exam Review Answer Section SHORT ANSWER 1. ANS: function domain: {Alice, Brad, Carl} range: {cat, dog} 2. ANS: not a function 3. ANS: function 4. ANS: not a function 5. ANS: 3 6. ANS: 4 7. ANS: -2x 2 + 3x ANS: 3x 2-11x ANS: all real numbers 10. ANS: {x x -4, 0, 4} 1
13 11. ANS: (f - g)(x) = -4x + 6; all real numbers 12. ANS: (f g)(x) = 12x 2-2x - 24; all real numbers 13. ANS: ANS: 15. ANS: not a function 16. ANS: function domain: {x x > 0} range: all real numbers intercept: (1, 0) symmetry: none 17. ANS: ANS: -3, 3.5, ANS: Yes 20. ANS: No 2
14 21. ANS: even 22. ANS: neither 23. ANS: odd 24. ANS: even 25. ANS: even 26. ANS: 3
15 27. ANS: 28. ANS: y = 29. ANS: y = 30. ANS: y = ANS: 32. ANS: {1, 2, 3, 4, 5, 8, 9} 4
16 33. ANS: {2, 3, 5} 34. ANS: {1, 2, 3, 4, 5, 9} 35. ANS: {0, 2, 3, 4, 5, 6, 7, 8, 9} 36. ANS: ANS: 38. ANS: ANS: 40. ANS: 41. ANS: 42. ANS: Not a polynomial 5
17 43. ANS: Polynomial; degree ANS: -3y 3 + 5y 2 + 5y ANS: 4x ANS: x 2-20x ANS: 3x 7-5x 3 ; remainder ANS: 6x - 7; remainder ANS: x 2 + 5; remainder ANS: (3x - 1)(3x + 1) 51. ANS: (3y - 1)(9y 2 + 3y + 1) 52. ANS: (x + 1) ANS: (9x - 7) ANS: 2(x + 2)(x - 3) 6
18 55. ANS: (2x + 3)(5x + 3) 56. ANS: x 4-3x 3 + 9x 2-26x + 78; remainder ANS: -3x 2 + 3x - 2; remainder ANS: Yes 59. ANS: No 60. ANS: 61. ANS: 4x ANS: ANS: ANS: ANS:
19 66. ANS: ANS: 68. ANS: No, no 69. ANS: No, no 70. ANS: f(x) = ; g(x) = x ANS: f(x) = ; g(x) = 5x ANS: {x 73. ANS: {x 74. ANS: One-to-one 75. ANS: No 8
20 76. ANS: No 77. ANS: Yes 78. ANS: {(-8, -4), (4, 8), (-2, -3), (2, 3)} D = {-8, 4, -2, 2}; R = {-4, 8, -3, 3} 79. ANS: 80. ANS: 81. ANS: Yes 9
21 82. ANS: Yes 83. ANS: f -1 (x) = 84. ANS: f -1 (x) = 85. ANS: f(x): D = {x x 2}, R = {y 0}; f -1 (x): D = {x x 0}, R = {y y 2} 86. ANS: Yes; degree ANS: Yes; degree ANS: f(x) = x 3 + 3x 2-4x - 12 for a = ANS: f(x) = x 3 + x 2-6x for a = ANS: 7, multiplicity 1, crosses x-axis; 5, multiplicity 4, touches x-axis 91. ANS: -2, multiplicity 1, crosses x-axis; 4, multiplicity 3, crosses x-axis 92. ANS: x-intercepts: 0, 2; y-intercept: 0 10
22 93. ANS: x-intercepts: -2, -5, 5; y-intercept: ANS: all real numbers 95. ANS: {x x -9, 4} 96. ANS: domain: {x x 2} range: {y y 3} 97. ANS: domain: {x x 0} range: all real numbers 98. ANS: 11
23 99. ANS: 100. ANS: x = -3, x = ANS: x =, x = ANS: none 103. ANS: none 12
24 104. ANS: 105. ANS: 106. ANS: (-, -7) 107. ANS: (-, -2) (2, 7) 13
25 ESSAY 108. ANS: 14
26 109. ANS: 15
11 /2 12 /2 13 /6 14 /14 15 /8 16 /8 17 /25 18 /2 19 /4 20 /8
MAC 1147 Exam #1a Answer Key Name: Answer Key ID# Summer 2012 HONOR CODE: On my honor, I have neither given nor received any aid on this examination. Signature: Instructions: Do all scratch work on the
More informationMAT116 Final Review Session Chapter 3: Polynomial and Rational Functions
MAT116 Final Review Session Chapter 3: Polynomial and Rational Functions Quadratic Function A quadratic function is defined by a quadratic or second-degree polynomial. Standard Form f x = ax 2 + bx + c,
More information. State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both.
PRECALCULUS MIDTERM PRACTICE TEST (2008-2009) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance d(, ) between the points and.
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) x 8. C) y = x + 3 2
Precalculus Fall Final Exam Review Name Date Period MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the expression. Assume that the variables
More informationSection Properties of Rational Expressions
88 Section. - Properties of Rational Expressions Recall that a rational number is any number that can be written as the ratio of two integers where the integer in the denominator cannot be. Rational Numbers:
More information1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.
Math120 - Precalculus. Final Review. Fall, 2011 Prepared by Dr. P. Babaali 1 Algebra 1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.
More informationFinal Exam Review. Determine whether the relation represents a function. If it is a function, state the domain and range.
Final Exam Review Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. 1) f(x) = x2-5 1) A) minimum; 0 B) minimum; -5 C) maximum;
More informationAP Calculus Summer Homework
Class: Date: AP Calculus Summer Homework Show your work. Place a circle around your final answer. 1. Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
More informationSection 5.1 Determine if a function is a polynomial function. State the degree of a polynomial function.
Test Instructions Objectives Section 5.1 Section 5.1 Determine if a function is a polynomial function. State the degree of a polynomial function. Form a polynomial whose zeros and degree are given. Graph
More informationUse a graphing utility to approximate the real solutions, if any, of the equation rounded to two decimal places. 4) x3-6x + 3 = 0 (-5,5) 4)
Advanced College Prep Pre-Calculus Midyear Exam Review Name Date Per List the intercepts for the graph of the equation. 1) x2 + y - 81 = 0 1) Graph the equation by plotting points. 2) y = -x2 + 9 2) List
More information1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.
Math120 - Precalculus. Final Review Prepared by Dr. P. Babaali 1 Algebra 1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents. (a) 5
More informationFinal Exam C Name i D) 2. Solve the equation by factoring. 4) x2 = x + 72 A) {1, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} 9 ± i
Final Exam C Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 7 ) x + + 3 x - = 6 (x + )(x - ) ) A) No restrictions; {} B) x -, ; C) x -; {} D) x -, ; {2} Add
More informationNAME DATE PERIOD. Power and Radical Functions. New Vocabulary Fill in the blank with the correct term. positive integer.
2-1 Power and Radical Functions What You ll Learn Scan Lesson 2-1. Predict two things that you expect to learn based on the headings and Key Concept box. 1. 2. Lesson 2-1 Active Vocabulary extraneous solution
More informationMidterm. Multiple Choice Identify the choice that best completes the statement or answers the question.
Midterm Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Factor completely. If the polynomial cannot be factored, say it is prime. 10x 2-95x + 225 2. Solve
More informationCumulative Review. Name. 13) 2x = -4 13) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Cumulative Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Evaluate the algebraic expression for the given value or values of the variable(s).
More informationA Partial List of Topics: Math Spring 2009
A Partial List of Topics: Math 112 - Spring 2009 This is a partial compilation of a majority of the topics covered this semester and may not include everything which might appear on the exam. The purpose
More informationFinal Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14
Final Exam A Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 1 1) x + 3 + 5 x - 3 = 30 (x + 3)(x - 3) 1) A) x -3, 3; B) x -3, 3; {4} C) No restrictions; {3} D)
More information1) The line has a slope of ) The line passes through (2, 11) and. 6) r(x) = x + 4. From memory match each equation with its graph.
Review Test 2 Math 1314 Name Write an equation of the line satisfying the given conditions. Write the answer in standard form. 1) The line has a slope of - 2 7 and contains the point (3, 1). Use the point-slope
More informationWhich one of the following is the solution to the equation? 1) 4(x - 2) + 6 = 2x ) A) x = 5 B) x = -6 C) x = -5 D) x = 6
Review for Final Exam Math 124A (Flatley) Name Which one of the following is the solution to the equation? 1) 4(x - 2) + 6 = 2x - 14 1) A) x = 5 B) x = -6 C) x = -5 D) x = 6 Solve the linear equation.
More information3 Polynomial and Rational Functions
3 Polynomial and Rational Functions 3.1 Polynomial Functions and their Graphs So far, we have learned how to graph polynomials of degree 0, 1, and. Degree 0 polynomial functions are things like f(x) =,
More informationPreCalculus Notes. MAT 129 Chapter 5: Polynomial and Rational Functions. David J. Gisch. Department of Mathematics Des Moines Area Community College
PreCalculus Notes MAT 129 Chapter 5: Polynomial and Rational Functions David J. Gisch Department of Mathematics Des Moines Area Community College September 2, 2011 1 Chapter 5 Section 5.1: Polynomial Functions
More informationMission 1 Simplify and Multiply Rational Expressions
Algebra Honors Unit 6 Rational Functions Name Quest Review Questions Mission 1 Simplify and Multiply Rational Expressions 1) Compare the two functions represented below. Determine which of the following
More informationName: Class: Date: A. 70 B. 62 C. 38 D. 46
Class: Date: Test 2 REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Divide: (4x 2 49y 2 ) (2x 7y) A. 2x 7y B. 2x 7y C. 2x 7y D. 2x 7y 2. What is
More informationDepartment of Mathematics, University of Wisconsin-Madison Math 114 Worksheet Sections (4.1),
Department of Mathematics, University of Wisconsin-Madison Math 114 Worksheet Sections (4.1), 4.-4.6 1. Find the polynomial function with zeros: -1 (multiplicity ) and 1 (multiplicity ) whose graph passes
More informationCatholic Central High School
Catholic Central High School Algebra II Practice Examination I Instructions: 1. Show all work on the test copy itself for every problem where work is required. Points may be deducted if insufficient or
More informationPre-Calculus Final Exam Review Units 1-3
Pre-Calculus Final Exam Review Units 1-3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the value for the function. Find f(x - 1) when f(x) = 3x
More informationSemester Review Packet
MATH 110: College Algebra Instructor: Reyes Semester Review Packet Remarks: This semester we have made a very detailed study of four classes of functions: Polynomial functions Linear Quadratic Higher degree
More informationPolynomial Degree Leading Coefficient. Sign of Leading Coefficient
Chapter 1 PRE-TEST REVIEW Polynomial Functions MHF4U Jensen Section 1: 1.1 Power Functions 1) State the degree and the leading coefficient of each polynomial Polynomial Degree Leading Coefficient y = 2x
More information2.6. Graphs of Rational Functions. Copyright 2011 Pearson, Inc.
2.6 Graphs of Rational Functions Copyright 2011 Pearson, Inc. Rational Functions What you ll learn about Transformations of the Reciprocal Function Limits and Asymptotes Analyzing Graphs of Rational Functions
More informationChapter 2 Polynomial and Rational Functions
Chapter 2 Polynomial and Rational Functions Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Quadratic Functions Polynomial Functions of Higher Degree Real Zeros of Polynomial Functions
More informationH-Pre-Calculus Targets Chapter I can write quadratic functions in standard form and use the results to sketch graphs of the function.
H-Pre-Calculus Targets Chapter Section. Sketch and analyze graphs of quadratic functions.. I can write quadratic functions in standard form and use the results to sketch graphs of the function. Identify
More informationf ( x ) = x Determine the implied domain of the given function. Express your answer in interval notation.
Test Review Section.. Given the following function: f ( ) = + 5 - Determine the implied domain of the given function. Epress your answer in interval notation.. Find the verte of the following quadratic
More informationChapter 1- Polynomial Functions
Chapter 1- Polynomial Functions WORKBOOK MHF4U W1 1.1 Power Functions MHF4U Jensen 1) Identify which of the following are polynomial functions: a) p x = cos x b) h x = 7x c) f x = 2x, d) y = 3x / 2x 0
More informationPolynomial and Rational Functions. Chapter 3
Polynomial and Rational Functions Chapter 3 Quadratic Functions and Models Section 3.1 Quadratic Functions Quadratic function: Function of the form f(x) = ax 2 + bx + c (a, b and c real numbers, a 0) -30
More informationChapter 2 Formulas and Definitions:
Chapter 2 Formulas and Definitions: (from 2.1) Definition of Polynomial Function: Let n be a nonnegative integer and let a n,a n 1,...,a 2,a 1,a 0 be real numbers with a n 0. The function given by f (x)
More informationNote: The actual exam will consist of 20 multiple choice questions and 6 show-your-work questions. Extra questions are provided for practice.
College Algebra - Unit 2 Exam - Practice Test Note: The actual exam will consist of 20 multiple choice questions and 6 show-your-work questions. Extra questions are provided for practice. MULTIPLE CHOICE.
More informationChapter 8. Exploring Polynomial Functions. Jennifer Huss
Chapter 8 Exploring Polynomial Functions Jennifer Huss 8-1 Polynomial Functions The degree of a polynomial is determined by the greatest exponent when there is only one variable (x) in the polynomial Polynomial
More informationAdvanced Algebra II 1 st Semester Exam Review
dname Advanced Algebra II 1 st Semester Exam Review Chapter 1A: Number Sets & Solving Equations Name the sets of numbers to which each number belongs. 1. 34 2. 525 3. 0.875 4. Solve each equation. Check
More informationRational Functions. Elementary Functions. Algebra with mixed fractions. Algebra with mixed fractions
Rational Functions A rational function f (x) is a function which is the ratio of two polynomials, that is, Part 2, Polynomials Lecture 26a, Rational Functions f (x) = where and are polynomials Dr Ken W
More informationMock Final Exam Name. Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) A) {- 30} B) {- 6} C) {30} D) {- 28}
Mock Final Exam Name Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) 1) A) {- 30} B) {- 6} C) {30} D) {- 28} First, write the value(s) that make the denominator(s) zero. Then solve the
More informationPolynomial Functions and Models
1 CA-Fall 2011-Jordan College Algebra, 4 th edition, Beecher/Penna/Bittinger, Pearson/Addison Wesley, 2012 Chapter 4: Polynomial Functions and Rational Functions Section 4.1 Polynomial Functions and Models
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Calculus I - Homework Chapter 2 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the graph is the graph of a function. 1) 1)
More informationMath 0320 Final Exam Review
Math 0320 Final Exam Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Factor out the GCF using the Distributive Property. 1) 6x 3 + 9x 1) Objective:
More informationSimplifying Rationals 5.0 Topic: Simplifying Rational Expressions
Simplifying Rationals 5.0 Topic: Simplifying Rational Expressions Date: Objectives: SWBAT (Simplify Rational Expressions) Main Ideas: Assignment: Rational Expression is an expression that can be written
More informationThe Graph of a Quadratic Function. Quadratic Functions & Models. The Graph of a Quadratic Function. The Graph of a Quadratic Function
8/1/015 The Graph of a Quadratic Function Quadratic Functions & Models Precalculus.1 The Graph of a Quadratic Function The Graph of a Quadratic Function All parabolas are symmetric with respect to a line
More informationCollege Algebra and College Algebra with Review Final Review
The final exam comprises 30 questions. Each of the 20 multiple choice questions is worth 3 points and each of the 10 open-ended questions is worth 4 points. Instructions for the Actual Final Exam: Work
More information6.1 Using Properties of Exponents 1. Use properties of exponents to evaluate and simplify expressions involving powers. Product of Powers Property
6.1 Using Properties of Exponents Objectives 1. Use properties of exponents to evaluate and simplify expressions involving powers. 2. Use exponents and scientific notation to solve real life problems.
More informationAlgebra I - Study Guide for Final
Name: Date: Period: Algebra I - Study Guide for Final Multiple Choice Identify the choice that best completes the statement or answers the question. To truly study for this final, EXPLAIN why the answer
More informationPower and Polynomial Functions. College Algebra
Power and Polynomial Functions College Algebra Power Function A power function is a function that can be represented in the form f x = kx % where k and p are real numbers, and k is known as the coefficient.
More information, a 1. , a 2. ,..., a n
CHAPTER Points to Remember :. Let x be a variable, n be a positive integer and a 0, a, a,..., a n be constants. Then n f ( x) a x a x... a x a, is called a polynomial in variable x. n n n 0 POLNOMIALS.
More informationTo get horizontal and slant asymptotes algebraically we need to know about end behaviour for rational functions.
Concepts: Horizontal Asymptotes, Vertical Asymptotes, Slant (Oblique) Asymptotes, Transforming Reciprocal Function, Sketching Rational Functions, Solving Inequalities using Sign Charts. Rational Function
More informationb) since the remainder is 0 I need to factor the numerator. Synthetic division tells me this is true
Section 5.2 solutions #1-10: a) Perform the division using synthetic division. b) if the remainder is 0 use the result to completely factor the dividend (this is the numerator or the polynomial to the
More informationChapter 5B - Rational Functions
Fry Texas A&M University Math 150 Chapter 5B Fall 2015 143 Chapter 5B - Rational Functions Definition: A rational function is The domain of a rational function is all real numbers, except those values
More informationUMUC MATH-107 Final Exam Information
UMUC MATH-07 Final Exam Information What should you know for the final exam? Here are some highlights of textbook material you should study in preparation for the final exam. Review this material from
More informationMathematics Precalculus: Academic Unit 1: Polynomial and Transcendental Functions
Understandings Questions Knowledge Functions can be used as models for real-life problems. Functions can be graphed, evaluated, transformed, analyzed, manipulated and combined using algebraic & graphical
More informationChapter 7 Polynomial Functions. Factoring Review. We will talk about 3 Types: ALWAYS FACTOR OUT FIRST! Ex 2: Factor x x + 64
Chapter 7 Polynomial Functions Factoring Review We will talk about 3 Types: 1. 2. 3. ALWAYS FACTOR OUT FIRST! Ex 1: Factor x 2 + 5x + 6 Ex 2: Factor x 2 + 16x + 64 Ex 3: Factor 4x 2 + 6x 18 Ex 4: Factor
More information6x 3 12x 2 7x 2 +16x 7x 2 +14x 2x 4
2.3 Real Zeros of Polynomial Functions Name: Pre-calculus. Date: Block: 1. Long Division of Polynomials. We have factored polynomials of degree 2 and some specific types of polynomials of degree 3 using
More informationUsing Properties of Exponents
6.1 Using Properties of Exponents Goals p Use properties of exponents to evaluate and simplify expressions involving powers. p Use exponents and scientific notation to solve real-life problems. VOCABULARY
More informationIntroduction. A rational function is a quotient of polynomial functions. It can be written in the form
RATIONAL FUNCTIONS Introduction A rational function is a quotient of polynomial functions. It can be written in the form where N(x) and D(x) are polynomials and D(x) is not the zero polynomial. 2 In general,
More informationMidterm Review. Name: Class: Date: ID: A. Short Answer. 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k.
Name: Class: Date: ID: A Midterm Review Short Answer 1. For each graph, write the equation of a radical function of the form y = a b(x h) + k. a) b) c) 2. Determine the domain and range of each function.
More informationReview all the activities leading to Midterm 3. Review all the problems in the previous online homework sets (8+9+10).
MA109, Activity 34: Review (Sections 3.6+3.7+4.1+4.2+4.3) Date: Objective: Additional Assignments: To prepare for Midterm 3, make sure that you can solve the types of problems listed in Activities 33 and
More informationMath 46 Final Exam Review Packet
Math 46 Final Exam Review Packet Question 1. Perform the indicated operation. Simplify if possible. 7 x x 2 2x + 3 2 x Question 2. The sum of a number and its square is 72. Find the number. Question 3.
More informationSolving Equations Quick Reference
Solving Equations Quick Reference Integer Rules Addition: If the signs are the same, add the numbers and keep the sign. If the signs are different, subtract the numbers and keep the sign of the number
More informationINSTRUCTIONS USEFUL FORMULAS
MATH 1100 College Algebra Spring 18 Exam 1 February 15, 2018 Name Student ID Instructor Class time INSTRUCTIONS 1. Do not open until you are told to do so. 2. Do not ask questions during the exam. 3. CAREFULLY
More information6.1 Polynomial Functions
6.1 Polynomial Functions Definition. A polynomial function is any function p(x) of the form p(x) = p n x n + p n 1 x n 1 + + p 2 x 2 + p 1 x + p 0 where all of the exponents are non-negative integers and
More informationPolynomial Expressions and Functions
Hartfield College Algebra (Version 2017a - Thomas Hartfield) Unit FOUR Page - 1 - of 36 Topic 32: Polynomial Expressions and Functions Recall the definitions of polynomials and terms. Definition: A polynomial
More informationSection 4.1: Polynomial Functions and Models
Section 4.1: Polynomial Functions and Models Learning Objectives: 1. Identify Polynomial Functions and Their Degree 2. Graph Polynomial Functions Using Transformations 3. Identify the Real Zeros of a Polynomial
More informationReteach Multiplying and Dividing Rational Expressions
8-2 Multiplying and Dividing Rational Expressions Examples of rational expressions: 3 x, x 1, and x 3 x 2 2 x 2 Undefined at x 0 Undefined at x 0 Undefined at x 2 When simplifying a rational expression:
More informationd. What are the steps for finding the y intercepts algebraically?(hint: what is equal to 0?)
st Semester Pre Calculus Exam Review You will not receive hints on your exam. Make certain you know how to answer each of the following questions. This is a test grade. Your WORK and EXPLANATIONS are graded
More informationPolynomials. Exponents. End Behavior. Writing. Solving Factoring. Graphing. End Behavior. Polynomial Notes. Synthetic Division.
Polynomials Polynomials 1. P 1: Exponents 2. P 2: Factoring Polynomials 3. P 3: End Behavior 4. P 4: Fundamental Theorem of Algebra Writing real root x= 10 or (x+10) local maximum Exponents real root x=10
More informationAlgebra II Midterm Exam Review Packet
Algebra II Midterm Eam Review Packet Name: Hour: CHAPTER 1 Midterm Review Evaluate the power. 1.. 5 5. 6. 7 Find the value of each epression given the value of each variable. 5. 10 when 5 10 6. when 6
More informationMATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline
MATH 0960 ELEMENTARY ALGEBRA FOR COLLEGE STUDENTS (8 TH EDITION) BY ANGEL & RUNDE Course Outline 1. Real Numbers (33 topics) 1.3 Fractions (pg. 27: 1-75 odd) A. Simplify fractions. B. Change mixed numbers
More informationExtra Polynomial & Rational Practice!
Extra Polynomial & Rational Practice! EPRP- p1 1. Graph these polynomial functions. Label all intercepts and describe the end behavior. 3 a. P(x = x x 1x. b. P(x = x x x.. Use polynomial long division.
More informationAdvanced Algebra 2 - Assignment Sheet Chapter 1
Advanced Algebra - Assignment Sheet Chapter #: Real Numbers & Number Operations (.) p. 7 0: 5- odd, 9-55 odd, 69-8 odd. #: Algebraic Expressions & Models (.) p. 4 7: 5-6, 7-55 odd, 59, 6-67, 69-7 odd,
More informationRational Exponents. Polynomial function of degree n: with leading coefficient,, with maximum number of turning points is given by (n-1)
Useful Fact Sheet Final Exam Interval, Set Builder Notation (a,b) = {x a
More informationAlgebra 2 Segment 1 Lesson Summary Notes
Algebra 2 Segment 1 Lesson Summary Notes For each lesson: Read through the LESSON SUMMARY which is located. Read and work through every page in the LESSON. Try each PRACTICE problem and write down the
More informationCHAPTER 8A- RATIONAL FUNCTIONS AND RADICAL FUNCTIONS Section Multiplying and Dividing Rational Expressions
Name Objectives: Period CHAPTER 8A- RATIONAL FUNCTIONS AND RADICAL FUNCTIONS Section 8.3 - Multiplying and Dividing Rational Expressions Multiply and divide rational expressions. Simplify rational expressions,
More informationSection 2: Polynomial and Rational Functions
Section 2: Polynomial and Rational Functions The following maps the videos in this section to the Texas Essential Knowledge and Skills for Mathematics TAC 111.42(c). 2.01 Quadratic Functions Precalculus
More informationAlgebra 2 Honors: Final Exam Review
Name: Class: Date: Algebra 2 Honors: Final Exam Review Directions: You may write on this review packet. Remember that this packet is similar to the questions that you will have on your final exam. Attempt
More informationALGEBRA 2 FINAL EXAM REVIEW
Class: Date: ALGEBRA 2 FINAL EXAM REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question.. Classify 6x 5 + x + x 2 + by degree. quintic c. quartic cubic d.
More informationMath 0310 Final Exam Review
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the linear equation and check the solution. 1) 13(x - 52) = 26 1) A) {26} B) {52} C) {50} D)
More information171S4.3 Polynomial Division; The Remainder and Factor Theorems. October 26, Polynomial Division; The Remainder and Factor Theorems
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial
More informationRange: y-values - output read y's from bottom to top (smallest to largest)
Domain & Range (card) 8 Domain: x-values - input read x's from left to rt. (smallest to largest) *some functions have domain restrictions - can't divide by zero to find: set the den. = 0 and solve for
More information171S4.3 Polynomial Division; The Remainder and Factor Theorems. March 24, Polynomial Division; The Remainder and Factor Theorems
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial
More information1) Solve the formula for the indicated variable. P = 2L + 2W for W. 2) Solve the formula for the variable y. 5 = 7x - 8y
Math120 Cumulative Review This is to help prepare you for the 40 question final exam. It is not all inclusive of the material covered in your course. Therefore items not on this review may appear on the
More informationPre-Algebra 2. Unit 9. Polynomials Name Period
Pre-Algebra Unit 9 Polynomials Name Period 9.1A Add, Subtract, and Multiplying Polynomials (non-complex) Explain Add the following polynomials: 1) ( ) ( ) ) ( ) ( ) Subtract the following polynomials:
More informationPart I: Multiple Choice Questions
Name: Part I: Multiple Choice Questions. What is the slope of the line y=3 A) 0 B) -3 ) C) 3 D) Undefined. What is the slope of the line perpendicular to the line x + 4y = 3 A) -/ B) / ) C) - D) 3. Find
More information2. If the discriminant of a quadratic equation is zero, then there (A) are 2 imaginary roots (B) is 1 rational root
Academic Algebra II 1 st Semester Exam Mr. Pleacher Name I. Multiple Choice 1. Which is the solution of x 1 3x + 7? (A) x -4 (B) x 4 (C) x -4 (D) x 4. If the discriminant of a quadratic equation is zero,
More informationChapter 3: Inequalities, Lines and Circles, Introduction to Functions
QUIZ AND TEST INFORMATION: The material in this chapter is on Quiz 3 and Exam 2. You should complete at least one attempt of Quiz 3 before taking Exam 2. This material is also on the final exam and used
More informationFinal Jeopardy! Appendix Ch. 1 Ch. 2 Ch. 3 Ch. 4 Ch. 5
Final Jeopardy! Appendix Ch. 1 Ch. Ch. 3 Ch. 4 Ch. 5 00 00 00 00 00 00 400 400 400 400 400 400 600 600 600 600 600 600 800 800 800 800 800 800 1000 1000 1000 1000 1000 1000 APPENDIX 00 Is the triangle
More informationFinal Exam Review for DMAT 0310
Final Exam Review for DMAT 010 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor the polynomial completely. What is one of the factors? 1) x
More informationSemester 1 Exam Review - Precalculus Test ID:
203-4 Semester Exam Review - Precalculus Test ID: Use interval notation to describe the interval of real numbers. ) x is greater than or equal to 0 and less than or equal to 4. ) A) [0, 4) B) (0, 4] C)
More informationQuestions From Old Exams
MATH 0 OLD EXAM QUESTIONS FOR EXAM 3 ON CHAPTERS 3 AND 4 PAGE Questions From Old Eams. Write the equation of a quadratic function whose graph has the following characteristics: It opens down; it is stretched
More informationChapter Five Notes N P U2C5
Chapter Five Notes N P UC5 Name Period Section 5.: Linear and Quadratic Functions with Modeling In every math class you have had since algebra you have worked with equations. Most of those equations have
More informationx 20 f ( x ) = x Determine the implied domain of the given function. Express your answer in interval notation.
Test 2 Review 1. Given the following relation: 5 2 + = -6 - y Step 1. Rewrite the relation as a function of. Step 2. Using the answer from step 1, evaluate the function at = -1. Step. Using the answer
More informationTest # 3 Review. È 3. Compare the graph of n 1 ÎÍ. Name: Class: Date: Short Answer. 1. Find the standard form of the quadratic function shown below:
Name: Class: Date: ID: A Test # 3 Review Short Answer 1. Find the standard form of the quadratic function shown below: 2. Compare the graph of m ( x) 9( x 7) 2 5 with m ( x) x 2. È 3. Compare the graph
More informationHorizontal and Vertical Asymptotes from section 2.6
Horizontal and Vertical Asymptotes from section 2.6 Definition: In either of the cases f(x) = L or f(x) = L we say that the x x horizontal line y = L is a horizontal asymptote of the function f. Note:
More informationReading Mathematical Expressions & Arithmetic Operations Expression Reads Note
Math 001 - Term 171 Reading Mathematical Expressions & Arithmetic Operations Expression Reads Note x A x belongs to A,x is in A Between an element and a set. A B A is a subset of B Between two sets. φ
More informationImportant Math 125 Definitions/Formulas/Properties
Exponent Rules (Chapter 3) Important Math 125 Definitions/Formulas/Properties Let m & n be integers and a & b real numbers. Product Property Quotient Property Power to a Power Product to a Power Quotient
More informationMAC College Algebra
MAC 05 - College Algebra Name Review for Test 2 - Chapter 2 Date MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact distance between the
More information