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### sso0103

Course: MATH 105, Fall 2009
School: Bellevue College
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Word Count: 644

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1.3 Shifting, Section Reflecting, and Stretching Graphs 29 Course Number Section 1.3 Shifting, Reflecting, and Stretching Graphs Instructor Objective: In this lesson you learned how to identify and graph shifts, reflections, and nonrigid transformations of functions. Date Important Vocabulary Define each term or concept. Vertical shift A transformation of the graph of y = f(x), represented by h(x) = f(x) c,...

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1.3 Shifting, Section Reflecting, and Stretching Graphs 29 Course Number Section 1.3 Shifting, Reflecting, and Stretching Graphs Instructor Objective: In this lesson you learned how to identify and graph shifts, reflections, and nonrigid transformations of functions. Date Important Vocabulary Define each term or concept. Vertical shift A transformation of the graph of y = f(x), represented by h(x) = f(x) c, in which the graph is shifted upward or downward c units respectively (c is a positive real number). Horizontal shift A transformation of the graph of y = f(x), represented by h(x) = f(x c), in which the graph is shifted to the left or to the right c units respectively (c is a positive real number). Rigid transformations Transformations in which the basic shape of the graph is unchanged. Nonrigid transformations Transformations that cause a distortion (a change in the original shape of the graph). I. Summary of Graphs of Common Functions (Page 100) Sketch an example of each of the six most commonly used functions in algebra. Constant Function y What you should learn How to recognize graphs of common functions Identity Function y x x Absolute Value Function y Square Root Function y x x Larson/Hostetler/Edwards Precalculus: Functions and Graphs, A Graphing Approach, 3rd Edition Student Success Organizer IAE Copyright Houghton Mifflin Company. All rights reserved. 30 Quadratic Function y Chapter 1 Functions and Their Graphs Cubic Function y x x II. Vertical and Horizontal Shifts (Pages 101-102) Let c be a positive real number. Complete the following representations of shifts in the graph of y = f (x) : 1) Vertical shift c units upward: h(x) = f(x) + c 2) Vertical shift c units downward: 3) Horizontal shift c units to the right: 4) Horizontal shift c units to the left: Example 1: h(x) = f(x) - c h(x) = f(x - c) h(x) = f(x + c) What you should learn How to use vertical and horizontal shifts to sketch the graphs of functions Let f x ( ) = x . Write the equation for the function resulting from a vertical shift of 3 units downward and a horizontal shift of 2 units to the right of the graph of f (x ) . f(x) = | x - 2 | - 3 III. Reflecting Graphs (Pages 103-104) A reflection in the x-axis is a type of transformation of the graph of y = f(x) represented by h(x) = - f(x) . A reflection in What you should learn How to use reflections to sketch the graphs of functions the y-axis is a type of transformation of the graph of y = f(x) represented by h(x) = f(- x) . Example 2: Let f ( x ) = x . Describe the graph of g ( x) = - x in terms of f . The graph of g is a reflection of the graph of f in the x-axis. Larson/Hostetler/Edwards Precalculus: Functions and Graphs, A Graphing Approach, 3rd Edition Student Success Organizer IAE Copyright Houghton Mifflin Company. All rights reserved. Section 1.3 Shifting, Reflecting, and Stretching Graphs 31 IV. Nonrigid Transformations (Page 105) Name three types of rigid transformations: 1) Horizontal shifts 2) Vertical shifts 3) Reflections Rigid transformations change only the graph in the xy-plane. Name two types of nonrigid transformations: 1) Vertical stretch 2) V...

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Bellevue College - MATH - 105
Section 3.3Properties of Logarithms61 Course Number InstructorSection 3.3 Properties of LogarithmsObjective: In this lesson you learned how to rewrite logarithmic functions with different bases and how to use properties of logarithms to evalua
Bellevue College - MATH - 105
Section P.3Lines in the Plane9 Course NumberSection P.3 Lines in the PlaneInstructor Objective: In this lesson you learned how to find and use the slope of a line to write and graph linear equations. DateImportant VocabularyDefine each ter
Bellevue College - MATH - 105
Chapter 1Functions and Their GraphsCourse Number Instructor DateSection 1.1 FunctionsObjective: In this lesson you learned how to evaluate functions and find their domains.Important VocabularyDefine each term or concept.Function A functi
Bellevue College - MATH - 105
Section P.2Graphs of Equations5 Course NumberSection P.2 Graphs of EquationsInstructor Objective: In this lesson you learned how to sketch graphs of equations by point plotting or using a graphing utility. DateImportant VocabularyDefine ea
Bellevue College - MATH - 105
Section 2.3Real Zeros of Polynomial Functions41 Course Number InstructorSection 2.3 Real Zeros of Polynomial FunctionsObjective: In this lesson you learned how to use long division and synthetic division to divide polynomials by other polynomi
Bellevue College - MATH - 105
Section 2.6Rational Functions and Asymptotes51 Course Number InstructorSection 2.6 Rational Functions and AsymptotesObjective: In this lesson you learned how to determine the domain and find asymptotes of rational functions.DateImportant V
Bellevue College - MATH - 105
Section 2.4Complex Numbers45 Course NumberSection 2.4 Complex NumbersInstructor Objective: In this lesson you learned how to perform operations with complex numbers and plot complex numbers in the complex plane. DateImportant VocabularyDef
Bellevue College - MATH - 105
Section P.4Solving Equations Algebraically and Graphically13 Course Number Instructor DateSection P.4 Solving Equations Algebraically and GraphicallyObjective: In this lesson you learned how to solve linear equations, quadratic equations, poly
Bellevue College - MATH - 105
Section 1.2Graphs of Functions25 Course NumberSection 1.2 Graphs of FunctionsInstructor Objective: In this lesson you learned how to analyze the graphs of functions. DateImportant VocabularyDefine each term or concept.Graph of a function
Bellevue College - MATH - 105
Section 1.4Combinations of Functions33 Course NumberSection 1.4 Combinations of FunctionsInstructor Objective: In this lesson you learned how to find arithmetic combinations and compositions of functions. DateImportant VocabularyDefine eac
Bellevue College - MATH - 105
Section 3.5Exponential and Logarithmic Models65 Course Number InstructorSection 3.5 Exponential and Logarithmic ModelsObjective: In this lesson you learned how to use exponential growth models, exponential decay models, Gaussian models, logist
Bellevue College - MATH - 105
Section 2.5The Fundamental Theorem of Algebra49 Course Number InstructorSection 2.5 The Fundamental Theorem of AlgebraObjective: In this lesson you learned how to determine the number of zeros of polynomial functions and find them.DateImpo
Bellevue College - MATH - 105
Chapter 3Exponential and Logarithmic FunctionsCourse Number InstructorSection 3.1 Exponential Functions and Their GraphsObjective: In this lesson you learned how to recognize, evaluate, and graph exponential functions.DateImportant Vocabul
Bellevue College - MATH - 105
766PART III: Solutions to Even-Numbered Exercises94. True. The degree of the numerator (3) is larger than the degree of the denominator (2). x2n 96. xn 3 x3n x3n6xn 27xn 27xn 18xn 9xn 9xn 279 27 98. A divisor divides evenly into the dividend
Bellevue College - MATH - 105
674PART III: Solutions to Even-Numbered Exercises10. The line appears to go through 0, 1 and 6, 5 . Slope y2 x2 y1 x1 5 6 1 0 2 312. Slope4 464 2(2, 4)414. Slope6 172 3(1, 6)8 42-612(4, - 4)-6-87(-3, -2)-316.
Whatcom Community College - MATH - 105
Section 2.2Polynomial Functions of Higher Degree39 Course Number InstructorSection 2.2 Polynomial Functions of Higher DegreeObjective: In this lesson you learned how to sketch and analyze graphs of polynomial functions.DateImportant Vocabu
Whatcom Community College - MATH - 105
Chapter 2Polynomial and Rational FunctionsCourse Number InstructorSection 2.1 Quadratic FunctionsObjective: In this lesson you learned how to sketch and analyze graphs of quadratic functions.DateImportant VocabularyDefine each term or co
Whatcom Community College - MATH - 105
739PART III: Solutions to Even-Numbered ExercisesReview Exercises for Chapter 1Solutions to Even-Numbered Exercises 2. (a) Not a function. u is assigned 2 different values. (b) Function (c) Function(d) Not a function. w is assigned 2 different
Whatcom Community College - MATH - 151
Math&amp; 151 Test 1 Review [0.2] Lines 1. Find the slope of the secant line passing through (2, f(2) and (2+h, f(2+h), where f (x) = 1- x 2 . 2. Find the shortest distance between (x -1) + (y - 2) = 4 and (x - 8) + (y -11) = 49 .2 2 2 23. Find the
Whatcom Community College - MATH - 151
151 Q3 review answer (2.1 &amp; 2.2)I can not guarantee that all of the following answers are 100% correct. If you got different answer or if you have any question, Please let me know before the quiz. Good luck! [Sketching the slope of graph] Slope:+ D
Whatcom Community College - MATH - 099
Math 099 Test 1 Review (Chp1 &amp; Chp 2)1. Graph the equation in the window you chose. y x - =1 Both intercepts should be visible. 12 20 a. What is your window scale? b. What is x-intercept and y-intercept? 2. 3x - 4 y = 12 a. Find the intercepts of
Whatcom Community College - MATH - 151
2.3 Power Rule, derivative of trig function and ex function.2.3 Power Rule , trig function and e x function Power Rule : ( f n ) = nf n-1 f Trig function : (tanx ) = sec 2 x(secx ) = secx tan x (cscx ) = cscx cot x(cotx ) = -csc 2 xD
Whatcom Community College - MATH - 151
151 Quiz 3 Review[Sketching the slope of graph] 1. Sketch the graph of the derivative of the function graphed below.| -||||||||| -||||||||[Interpretation of derivative] 1. A slug is moving across Cathy's garden
Whatcom Community College - MATH - 099
Math 099 Test3 review answerm9 7n 6 7 1.(2) &quot;4a1.(1) 1.(3)10.(4) x &quot; 3 11. log 6 Q = 3y &quot; 4rb3 2! !7!!1.(4)t4912. y = 7 13.(1) 5 13.(2) 2! !! !2.(1) 27k 20 2.(2) &quot;2y 2.(3) 6 2.(4) 2.(5)!3 2x x2 &quot; 214.(1) \$500,000 14
Whatcom Community College - MATH - 099
099 Quiz 3 Review (3.4, 3.5 &amp; 3.6)1. We want to graph y = x 2 &quot; 6x + 5 . Answer the following questions. (1) Find x- intercept.!(2) Find y-intercept. (3) Find the vertex.(4) Name the shape of the graph. (5) Graph it showing all the point you f
Whatcom Community College - MATH - 099
Winter 2007 Math 099 Final Answers 1. 2. 3. 4. 5. 6. -1 7. 8. 6 9. 1/8 10. m = 2/5 11. neither 12. 13. 2(2x 1)(x 3) 14. 2 15. 16. 17. x = 33 18. x = 38/3 19. x = 14 20. x = 21. 22. x = -2/3, x = 1 23. (5, -2) 24. 20 sec 25. 26. 4.5 hrs 27a. 82 27b
Whatcom Community College - MATH - 099
Winter 2006 Math 099 Final Answers 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20a. 5 20b. 4 20c. 20d. 21a. parabola 21b. (0, 5) 21c. (1, 0) and (5, 0) 21d. (3, -4) 21e. (6, 5) 22b. [0, 4] 23. 24. 16 hrs 25. 42 in 26a. 65 26b.
Whatcom Community College - MATH - 151
Test 2 Review Answer1.2 &amp; 1.3 1. (1) 2 (2) 0 (3) -1 (4) -1 (5) -4 (6) -25 (7) -1 (8) x = 0, 2, 3 -2 2(x - 3) (1) = no limit x-3 2. 2 x -5x&lt;3 2(x - 3) x = 3 . so lim = -2 x 2 x-3 x&gt;3(2) lim- [ x -1] = [-5.00001-1] = [-6.00001] = -73. (1) u
Whatcom Community College - MATH - 151
2.4 &amp; 2.5 Applications1. A ball at the end of a rubber band is oscillating up and down.t And its height (in feet) above the floor at time t seconds is h(t) = 5 + 2sin . 2 (1) How fast is the ball travelling and it the ball moving up or down afte
Whatcom Community College - MATH - 151
1. A duck is hiding in the bushes. A dog passes by the bushes and the duck flies upward to escape 10 from the dog, then lands in a pond, a safe distance from the dog. The duck's height, s in meters after t seconds is shown in the graph.
Whatcom Community College - MATH - 151
1. 1) I picked (1, 6) and (2, 10.8). Then the slope is 4.8. Your answers may vary depending on the points you set. But should be close enough to 4.8. 2) Tangent slope at t=3. (3,6) is obvious and I picked (2.8, 7) as a point close to (3, 6). Slope m
Whatcom Community College - MATH - 151
Math&amp; 151 Quiz 1 Review1. Graph f (x) = (x - 3) 2 . Then graph g(x) = f (x) - 2 and h(x) = f (x) - 2 Specify x-intercepts and y-intercepts for each graph.2. Define A(x) to be the area of the rectangle under the line y=3 and above the xaxis,
Whatcom Community College - MATH - 151
T13171 7690 8332 4568 1950 1256 5448 6161 4540 9466 8037 7279 3933 9604 2469 3273 1440 2071 8735 8033 1107 8834 4464 3721 1670 339 2953 8657 4789 7176 8182 9886 9799 7298 6816 2092 7738 9802 3283 798 3138 4512 9541 4333 4179 90 87 60 82 82 85 74 75
Whatcom Community College - MATH - 151
Math&amp; 151_Derivative Derivative Notationf (x), D( f (x), df (x) dxDefinition f (x + h) - f (x) f (x) = lim h 0 h Graphically f (x) is the slope of the tangent line In Application The rate of change of the function Techniques (Formula) to find de
Whatcom Community College - MATH - 105
Section P.5Solving Inequalities Algebraically and Graphically17 Course NumberSection P.5 Solving Inequalities Algebraically and GraphicallyObjective: In this lesson you learned how to solve linear inequalities, inequalities involving absolute
Whatcom Community College - MATH - 105
Section 3.2Logarithmic Functions and Their Graphs57 Course Number InstructorSection 3.2 Logarithmic Functions and Their GraphsObjective: In this lesson you learned how to recognize, evaluate, and graph logarithmic functions.DateImportant V
Whatcom Community College - MATH - 105
Section 1.3Shifting, Reflecting, and Stretching Graphs29 Course NumberSection 1.3 Shifting, Reflecting, and Stretching GraphsInstructor Objective: In this lesson you learned how to identify and graph shifts, reflections, and nonrigid transform
Whatcom Community College - MATH - 105
Section P.2Graphs of Equations5 Course NumberSection P.2 Graphs of EquationsInstructor Objective: In this lesson you learned how to sketch graphs of equations by point plotting or using a graphing utility. DateImportant VocabularyDefine ea
Whatcom Community College - MATH - 105
Section 2.3Real Zeros of Polynomial Functions41 Course Number InstructorSection 2.3 Real Zeros of Polynomial FunctionsObjective: In this lesson you learned how to use long division and synthetic division to divide polynomials by other polynomi
Whatcom Community College - MATH - 105
Section 2.6Rational Functions and Asymptotes51 Course Number InstructorSection 2.6 Rational Functions and AsymptotesObjective: In this lesson you learned how to determine the domain and find asymptotes of rational functions.DateImportant V
Whatcom Community College - MATH - 105
Section 2.4Complex Numbers45 Course NumberSection 2.4 Complex NumbersInstructor Objective: In this lesson you learned how to perform operations with complex numbers and plot complex numbers in the complex plane. DateImportant VocabularyDef
Whatcom Community College - MATH - 105
Section 1.2Graphs of Functions25 Course NumberSection 1.2 Graphs of FunctionsInstructor Objective: In this lesson you learned how to analyze the graphs of functions. DateImportant VocabularyDefine each term or concept.Graph of a function
Whatcom Community College - MATH - 105
Section 1.4Combinations of Functions33 Course NumberSection 1.4 Combinations of FunctionsInstructor Objective: In this lesson you learned how to find arithmetic combinations and compositions of functions. DateImportant VocabularyDefine eac
Whatcom Community College - MATH - 105
Section 3.5Exponential and Logarithmic Models65 Course Number InstructorSection 3.5 Exponential and Logarithmic ModelsObjective: In this lesson you learned how to use exponential growth models, exponential decay models, Gaussian models, logist
Whatcom Community College - MATH - 105
Section 2.5The Fundamental Theorem of Algebra49 Course Number InstructorSection 2.5 The Fundamental Theorem of AlgebraObjective: In this lesson you learned how to determine the number of zeros of polynomial functions and find them.DateImpo
Whatcom Community College - MATH - 105
Chapter 3Exponential and Logarithmic FunctionsCourse Number InstructorSection 3.1 Exponential Functions and Their GraphsObjective: In this lesson you learned how to recognize, evaluate, and graph exponential functions.DateImportant Vocabul
Whatcom Community College - MATH - 105
787PART III: Solutions to Even-Numbered Exercises92.794.-2054-6 -16 -11Domain: all x Range: y 6Domain: all x Range: y 0Review Exercises for Chapter 2Solutions to Even-Numbered Exercises 2. (a) y x 2 4 Vertical shift 4 units
Whatcom Community College - MATH - 105
Section 2.7Graphs of Rational Functions53 Course Number InstructorSection 2.7 Graphs of Rational FunctionsObjective: In this lesson you learned how to sketch graphs of rational functions.DateImportant VocabularyDefine each term or concep
Whatcom Community College - CS - 210
Washington - MATH - 409
HW 7 commentsOverall people did very well-most seemed to be understanding how approach these problems. A handful of people weren't specific enough for part A-they didn't specifically identify the set N_A(U) for which the cardinality of that an
Washington - SOC - 287
SOC 287: Sociology of Sexuality Study Guide Exam 2 The exam consists of 50 multiple choice and True/False questions. Expect questions from all of the readings, lectures and films. You will need to bring a mark sense form and a pencil. This study guid
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Harvard - MATHE - 311
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