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Chapter 1 Linear Functions efficiently. Evaluate. Question 1. Question 2. 4 – 2(3 + 2)2 Question 3. Question 4. Question 5. Question 6. Answer: Graph the transformation of the figure. Question 7. Question 8. Answer: Question 9. Answer: Question 10. Linear Functions Maintaining Mathematical PracticesMonitoring Progress Use a graphing calculator to graph the equation using the standard viewing window and a square viewing window. Describe any differences in the graphs. Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Answer: Determine whether the viewing window is square. Explain. Question 7. Question 8. Question 9. Question 10. Question 11. Question 12. Lesson 1.1 Parent Functions and TransformationsEssential Question What are the characteristics of some of the basic parent functions? EXPLORATION 1 Communicate Your Answer Question 2. Question 3. b. y = √x c. y = c y = e^x y = x³ y = x y = 1/x y = x² 1.1 Lesson Monitoring Progress Question 1. Answer: Graph the function and its parent function. Then describe the transformation. Question 2. Question 3. Question 4. Graph the function and its parent function. Then describe the transformation. Question 5. Question 6. Question 7. Use a graphing calculator to graph the function and its parent function. Then describe the transformations Question 8. Question 9. Question 10. Parent Functions and Transformations 1.1 ExercisesVocabulary and Core Concept Check Question 1. Question 2. Answer: Monitoring Progress and Modeling with Mathematics In Exercises 3–6, identify the function family to which f belongs. Compare the graph of f to the graph of its parent function. Question 3. Answer: Question 4. Answer: Question 5. Answer: Question 6. Answer: Question 7. Question 8. In Exercises 9–18, graph the function and its parent function. Then describe the transformation. Question 9. Question 10. Question 11. Question 12. Question 13. Question 14. Question 15. Question 16. Question 17. Question 18. In Exercises 19–26, graph the function and its parent function. Then describe the transformation. Question 19. Question 20. Question 21. Question 22. Question 23. Question 24. Question 25. Question 26. In Exercises 27–34, use a graphing calculator to graph the function and its parent function. Then describe the transformations. Question 27. Question 28. Question 29. Question 30. Question 31. Question 32. Question 33. Question 34. ERROR ANALYSIS In Exercises 35 and 36, identify and correct the error in describing the transformation of the parent function. Question
35. Answer: Question 36. Answer: MATHEMATICAL CONNECTIONS In Exercises 37 and 38, find the coordinates of the figure after the transformation. Question 37. Answer: Question 38. Answer: USING TOOLS In Exercises 39–44, identify the function family and describe the domain and range. Use a graphing calculator to verify your answer. Question 39. Question 40. Question 41. Question 42. Question 43. Question 44. Question 45. Answer: Question 46. Question 47. Question 48. a. Does the graph of g represent a vertical stretch or a vertical shrink of the graph of f? Explain your reasoning. b. Describe how to transform the graph of f to obtain the graph of h. Answer: Question 49. Question 50. Answer: Question 51. Question 52. Answer: Question 53. Question 54. Answer: Maintaining Mathematical Proficiency Determine whether the ordered pair is a solution of the equation. (Skills Review Handbook) Question 55. Question 56. Question
57. Question 58. Find the x-intercept and the y-intercept of the graph of the equation. (Skills Review Handbook) Question 59. Question 60. Question 61. Question 62. Lesson 1.2 Transformations of Linear and Absolute Value FunctionsEssential Question How do the graphs of y = f(x) + k, y = f(x – h), and y = -f(x) compare to the graph of the parent function f? EXPLORATION 1 y = | x | + k Transformation to the graph of the parent function f(x) = | x |. EXPLORATION 2 EXPLORATION 3 Communicate Your Answer Question 4.
Question 5. 1.2 Lesson Monitoring Progress Write a function g whose graph represents the indicated transformation of the graph of f. Use a graphing calculator to check your answer. Question 1. Question 2. Question 3. Question 4. Write a function g whose graph represents the indicated transformation of the graph of f. Use a graphing calculator to check your answer. Question
5. Question 6. Question 7. Question 8. Transformations of Linear and Absolute Value Functions 1.2 ExercisesVocabulary and Core Concept Check Question 1. Question 2. Answer: Monitoring Progress and Modeling with Mathematics In Exercises 3–8, write a function g whose graph represents the indicated transformation of the graph of f. Use a graphing calculator to check your answer. Question 3. Question 4. Question 5. Question 6. Question 7. Answer: Question 8. Answer: Question 9. Answer: Question 10. Answer: In Exercises 11–16, write a function g whose graph represents the indicated transformation of the graph of f. Use a graphing calculator to check your answer. Question 11. Question 12. Question 13. Question 14. Question 15. Question 16. In Exercises 17–22, write a function g whose graph represents the indicated transformation of the graph of f. Use a graphing calculator to check your answer. Question 17. Question 18. Question 19. Question 20. Question 21. Answer: Question 22. Answer: ANALYZING RELATIONSHIPS In Exercises 23–26, match the graph of the
transformation of f with the correct equation shown. Explain your reasoning. Question 23. Answer: Question 24. Answer: Question 25. Answer: Question 26. Answer: A. y = 2f(x) B. y = f(2x) C. y = f(x + 2) D. y = f(x) + 2 In Exercises 27–32, write a function g whose graph represents the indicated transformations of the graph of f. Question 27. Question 28. Question
29. Question 30. Question 31. Answer: Question 32. Answer: ERROR ANALYSIS In Exercises 33 and 34, identify and correct the error in writing the function g whose graph represents the indicated transformations of the graph of f. Question
33. Answer: Question 34. Answer: Question 35. Question 36. MATHEMATICAL CONNECTIONS For Exercises 37–40, describe the transformation of the graph of f to the graph of g. Then find the area of the shaded triangle. Question
37. Answer: Question 38. Answer: Question 39. Answer: Question 40. Answer: Question 41. Question 42. a. Reflect the graph of f in the y-axis. b. Shrink the graph of f vertically by a factor of \(\frac{1}{3}\). c. Stretch the graph of f horizontally by a factor of 2. Answer: Question 43. Question 44. Question 45. Maintaining Mathematical Proficiency Evaluate the function for the given value of x. (Skills Review Handbook) Question 46. Question 47. Question
48. Question 49. Create a scatter plot of the data. (Skills Review Handbook) Question 50. Answer: Question 51. Answer: Linear Functions Study Skills Taking Control of Your Class Time1.1 – 1.2 What Did You Learn? Core Vocabulary Core Concepts Section 1.1 Section 1.2 Mathematical Practices Question 1. Question 2. Study Skills Taking Control of Your Class Time Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Linear Functions 1.1-1.2 QuizIdentify the function family to which g belongs. Compare the graph of the function to the graph of its parent function. (Section 1.1) Question 1. Question 2. Question 3. Graph the function and its parent function. Then describe the transformation. (Section 1.1) Question 4. Question 5. Question 6. Answer: Question 7. Question 8. Question 9. Write a function g whose graph represents the indicated transformation of the graph of f. (Section 1.2) Question 10. Question 11. Question 12. Question 13. Write a function g whose graph represents the indicated transformations of the graph of f. (Section 1.2) Question 14. Question 15. Question 16. Question 17. Question 18. Answer: From the given data in the above table, 2 months = 2300 1 month = 2300/2 = 1150 12 months = 1150 × 12 = 13800 The mileage after 1 year is 13800. The estimated mileage after 1 year is 14,000 miles. Question 19. Lesson 1.3 Modeling with Linear FunctionsEssential Question EXPLORATION 1 Answer: m = 12,000 – 10,750 = $1,250 b = 12,000 V = -1250t + 12,000 The slope shows that for every year that passes, the value depreciates by $1250 EXPLORATION 2 Work with a partner. Match each description of the situation with its corresponding graph. Explain your reasoning. a. A person gives $20 per week to a friend to repay a $200 loan. b. An employee receives $12.50 per hour plus $2 for each unit produced per hour. c. A sales representative receives $30 per day for food plus $0.565 for each mile driven. d. A computer that was purchased for $750 depreciates $100 per year. Communicate Your Answer Question 3. Question 4. Answer:
b. The real life example of straight line depreciation is the decrease of speed of car by ten meter per second which was moving with an initial speed of a hundred meter per second till speed reaches thirty meter per second. 1.3 Lesson Monitoring Progress Question 1. Answer: Question 2. Question 3. a. Do the data show a linear relationship? If so, write an equation of a line of fit and use it to estimate the height of a female whose humerus is 40 centimeters long. b. Use the linear regression feature on a graphing calculator to find an equation of the line of best fit for the data. Estimate the height of a female whose humerus is 40 centimeters long. Compare this height to your estimate in part (a). Answer: Modeling with Linear Functions 1.3 ExercisesQuestion 1. Question 2. Monitoring Progress and Modeling with Mathematics In Exercises 3–8, use the graph to write an equation of the line and interpret the slope. Question 3. Answer: Question 4. Answer: Question 5. Answer: Question 6. Answer: Question 7. Answer: Question 8. Answer: Question 9. Answer: Question 10. ERROR ANALYSIS In Exercises 11 and 12, describe and correct the error in interpreting the slope in the context of the situation. Question 11. Answer: Question 12. Answer: In Exercises 13–16, determine whether the data show a linear relationship. If so, write an equation of a line of fit. Estimate y when x = 15 and explain its meaning in the context of the situation. Question 13. Answer: Question 14. Answer: Question 15. Answer: Question 16. Answer: Question 17. Answer: Question 18. Answer: USING TOOLS In Exercises 19–24, use the linear regression feature on a graphing calculator to find an equation of the line of best fit for the data. Find and interpret the correlation coefficient. Question 19. Answer: Question 20. Answer: Question 21. Answer: Question 22. Answer: Question 23. Answer: Question 24. Answer: Question 25. Question 26. a. What is the slope of the line? What does the slope represent? Answer: According to the graph (0, 30), (24, 0) are on the line. We can assume the slope is k. k = 30-0/0-24 = -5/4 And the slope represents the amount of money to be paid monthly. b. What is the domain and range of the function? What does each represent? c. How much do you still owe after making payments for 12 months? Question 27. Question 28. Question 29. Question 30. Question 31. Answer: Question 32. Answer: Maintaining Mathematical Proficiency Solve the system of linear equations in two variables by elimination or substitution. (Skills Review Handbook) Question 33. Question 34. Question 35. Question 36. Question 37. Question 38. Lesson 1.4 Solving Linear SystemsEssential Question EXPLORATION
1 Answer: 4x – 6y = 6 b. 2x – 3y = 3 Answer: 2x – 3y = 3 c. 2x – 3y = 3 Answer: 4x – 6y = 6 EXPLORATION 2 Answer: 2x + y = 5 x – y = 1 3x = 6 x = 2 2 – y = 1 2 – 1 = y y = 1 The linear system has one solution. b. x+ 3y = 1 Answer: x+ 3y = 1 -x + 2y = 4 5y = 5 y = 1 x + 3 = 1 x = 1 – 3 x = -2 The linear system has one solution. c. x + y = 0 Answer: 2x + 2y = 0 Communicate Your Answer Question 3. Question 4. Suppose you were given a system of three linear equations in three variables. Explain how you would approach solving such a system. Answer:
Question 5. Answer: x + y + z = 1 x – y – z = 3 -x – y – z = -1 Solving 1 & 2 x + y + z = 1 x – y – z = 3 2x = 4 x = 4/2 x = 2 x – y – z = 1 -x – y – z = -1 -2y -2z = 0 y + z = 0 y = -z 1.4 Lesson Monitoring Progress Question 1. Question
2. Question 3. Question 4. Question 5. Solving Linear Systems 1.4 ExercisesVocabulary and Core Concept Check Question 1. Question 2. Monitoring Progress and Modeling with Mathematics In Exercises 3–8, solve the system using the elimination method. Question 3. Question 4. 2x + 6y – 12z = -2 2x – y + 2z = -7 21y – 42z = 15 -x + 2y – 4z
= 5 Question 5. Question 6. Answer: Question 7. Question 8. ERROR ANALYSIS In Exercises 9 and 10, describe and correct the error in the first step of solving the system of linear equations. Question 9. Answer: Question 10. Answer: In Exercises 11–16, solve the system using the elimination method. Question 11. Question 12. Question 13. Question 14. Question 15. Question 16. Question 17. Answer: Question 18. Answer: In Exercises 19–28, solve the system of linear equations using the substitution method. Question 19. Question 20. Question 21. Question 22. Question 23. Question 24. Question 25. Question 26. Question 27. Question 28. Question 29. Answer: Question 30. Answer: Question 31. Question 32. MATHEMATICAL CONNECTIONS In Exercises 33 and 34, write and use a linear system to answer the question. Question 33. Answer: Question 34. Answer: Question 35. Question 36. Question 37. Answer: Question 38. Question 39. Question 40. Answer: Question 41. Question 42. Question 43. Answer: Maintaining Mathematical Proficiency Simplify. (Skills Review Handbook) Question 44. Question 45. Question 46. Question 47. Write a function g described by the given transformation of f(x) =∣x∣− 5.(Section 1.2) Question 48. Question 49. Question 50. Question 51. Linear Functions Performance Task: Secret of the Hanging Baskets1.3–1.4 What Did You Learn? Core Vocabulary Core Concepts Mathematical Practices Question 1. Question 2. Question 3. Performance Task Secret of the Hanging Baskets To explore the answers to this question and more, go to BigIdeasMath.com. Linear Functions Chapter ReviewGraph the function and its parent function. Then describe the transformation. Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Write a function g whose graph represents the indicated transformations of the graph of f. Use a graphing calculator to check your answer. Question 7. Question 8. Question 9. Question 10. Question 11. Question 12. Question 13. Question 14. Question 15. Question 16. Question 17. Question 18. Linear Functions Chapter TestWrite an equation of the line and interpret the slope and y-intercept. Question 1. Question 2. Solve the system. Check your solution, if possible. Question 3. Question 4. Question 5. Graph the function and its parent function. Then describe the transformation. Question 6. Question 7. Question 8. Match the transformation of f(x) = x with its graph. Then write a rule for g. Question 9. Question 10. Question 11. Question 12. Question 13. Linear Functions Cumulative AssessmentQuestion 1. Question 2. a. Verify that the data show a linear relationship. Then write an equation of a line of fit. b. Interpret the slope and y-intercept in this situation. c. Predict the cost of tuition in 2015. Question 3. Answer: From the graph, the correlation coefficient is r = -0.86 So, my friend is not correct, since the correlation coefficient is close to -1. Question 4. Question 5. Question 6. Question 7. Question
8. |