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{{ 'ml-book-overview-btn-show-description' | message }} {{ 'ml-book-overview-btn-save-textbook' | message }} Big Ideas Math Algebra 1 A Bridge to Success is a textbook from Big Ideas Math. Its ISBN is 9781680331141. The authors of the textbook are Larson and Boswell. Big Ideas Math Algebra 1 includes all topics in the Algebra 1 curriculum which was researched and developed by Boswell and Larson in cooperation with Big Ideas Learning. The chapters included in the textbook are on solving linear equations, solving linear inequalities, graphing linear functions, writing linear functions, solving systems of linear equations, exponential functions and sequences, polynomial equations and factoring, graphing quadratic equations, solving quadratic equations, radical functions and equations, and data analysis and displays. Using Mathleaks is like having a private tutor that is available whenever needed. Being focused on teaching the methods behind math and students learning rather than just memorizing, students are given a way to deeper understanding of the material. Mathleaks has thorough explanations, theories, and methodology for every solution and problem in the book, which makes it more useful than using an online calculator, graphing calculator, or math solver. With pedagogical and highly educational solutions written by licensed math educators, students are given hints and explanations to gain a complete understanding of the textbook material. As educational and affordable homework help that is focused on quality, parents and students can get help both in a traditional classroom setting and with remote learning. Seeking help on the Big Ideas Math Algebra 1 Answers Chapter 4 Writing Linear Functions? Then, this is the place as we have curated the Big Ideas Math Book Algebra 1 Answer Key Ch 4 Writing Linear Functions in a simple and understandable language. Ace up your preparation using the Writing Linear Functions BIM Algebra 1 Solutions Key via quick links
available. Become Pro in the concepts of Algebra Ch 4 Writing Linear Functions and seek the homework help needed. Enhance your subject knowledge in the Big Ideas Math Algebra 1 Answers Ch 4 Writing Linear Functions and practice on a regular basis. You will find Questions from Exercises, Practice Tests, Cumulative Assessment, Review Tests, Quiz, etc. in the Big Ideas Math Book Algebra 1 Chapter 4
Writing Linear Functions Answers. All the Solutions in the Writing Linear Functions Big Ideas Math Algebra 1 Answer Key are explained in detail as per the Common Core Curriculum. Get instant homework help needed using the Big Ideas Math Book Algebra 1 Answer Key Ch 4 and have an idea of all the concepts in it. Try to solve all the questions from the Big Ideas Math Textbooks Algebra 1 on your own and cross-check with the solutions provided. Assess your preparation standards and identify the
knowledge gap and concentrate on the areas you are lagging in. Practice using the Big Ideas Math Algebra 1 Chapter 4 Writing Linear Functions Solutions Key and score better grades in your exams. Use the graph to answer the question. Question 1. Answer: Explanation: Question 2. Answer: Explanation: question 3. Answer: Explanation: Question 4. Answer: Explanation: Solve the equation for y. Question 5. Answer: Explanation: Question 6. Answer: Explanation: Question 7. Answer: Explanation: Question 8. Answer: Explanation: Question 9. Answer: Explanation: Question 10. Answer: Explanation: Question 11. Answer: Monitoring Progress Question 1. Answer: Explanation: Question 2. Answer: Explanation: Question 3. Answer: Explanation: Essential
Question Given the graph of a linear function, how can you write an equation of the line? EXPLORATION 1 EXPLORATION 2 Mathematical Modeling Work with a partner. The graph shows the cost of a smartphone plan. a. What is the y-intercept of the line? Interpret the y-intercept in the context of the problem. b. Approximate the slope of the line. Interpret the slope in the context of the problem. c. Write an equation that represents the cost as a function of data usage. Communicate Your Answer Question 3. Question 4. The line passes through the points (0, -50), (300,0) m = 0+50/300-0 m = 50/300 m = 1/6 c = -50 y = mx + c y = 1/6x – 50 4.1 Lesson Monitoring Progress Write an equation of the line with the given slope and y-intercept. Question 1. Answer: Explanation: Question 2. Answer: Explanation: Write an equation of the line in slope-intercept form. Question 3. Answer: Explanation: Question 4. Answer: Explanation: Question 5. Explanation: Question 6. Explanation: Monitoring Progress Question 7. Explanation: Writing Equations in Slope-Intercept Form 4.1 ExercisesQuestion 1. Question 2. Answer: Explanation: Monitoring Progress and Modeling with Mathematics In Exercises 3–8, write an equation of the line with the given slope and y-intercept. Question 3. Question
4. Answer: Explanation: Question 5. Question 6. Answer: Explanation: Question 7. Question 8. Answer: Explanation: In Exercises 9–12, write an equation of the line in slope-intercept form. Question 9. Answer: Question 10. Answer: Explanation: Question 11. Answer: Question 12. Answer: Explanation: In Exercises 13–18, write an equation of the line that passes through the given points. Question 13. Question 14. Answer: Explanation: Question 15. Question 16. Answer: Explanation: Question 17. Question 18. Answer: Explanation: In Exercises 19–24, write a linear function f with the given values. Question 19. Question 20. Answer: Explanation: Question 21. Question 22. Answer: Explanation: Question 23. Question 24. Answer: Explanation: In Exercises 25 and 26, write a linear function f with the given values. Question 25. Answer: Question 26. Answer: Explanation: Question 27. Answer: Question 28. Answer: Slope = \(\frac { 1 – 4 }{ 5 – 0 } \) = \(\frac { -3 }{ 5 } \) y = \(\frac { -3 }{ 5 } \)x + 4 Question 29. Question 30. Answer: a. y = 75x + 50 b. It is less expensive to purchase a music software Explanation: Question 31. Question 32. Answer: Let us take x as the time and y as the distance covered. A person starts jogging from 20 meters. The person reaches 80 kilometers in 4 hours. Question 33. Question 34. Question 35. Answer: Question 36. a. Estimate the slope and y-intercept of the graph. b. Interpret your answers in part (a) in the context of the problem. c. How can you use your answers in part (a) to predict the U.S. box office revenue in 2018? Answer: Explanation: Question 37. Maintaining Mathematical Proficiency Solve the equation. (Section 1.3) Question 38. Answer: Explanation: Question 39. Question 40. Answer: Explanation: Question 41. Use intercepts to graph the linear equation. (Section 3.4) Question 42. Answer: Explanation: Question 43. Question 44. Answer: Explanation: Question
45. Lesson 4.2 Writing Equations in Point-Slope FormEssential Question EXPLORATION 1
EXPLORATION 2 EXPLORATION 3 Communicate Your Answer Question 4. Question 5. 4.2 Lesson Monitoring Progress Write an equation in point-slope form of the line that passes through the given point and has the given slope. Question 1. Answer: Explanation: Question 2. Answer: Explanation: Write an equation in slope-intercept form of the line that passes through the given points. Question 3. Answer: Explanation: Question 4. Answer: Explanation: Question 5. Answer: Explanation: Question 6. Answer: Explanation: Writing Equations in Point-Slope Form 4.2 ExercisesVocabulary and Core Concept Check Question 1. Question 2. Answer: Monitoring Progress and Modeling with Mathematics In Exercises 3−10, write an equation in point-slope form of the line that passes through the given point and has the given slope. Question 3. Question 4. Answer: Explanation: Question 5. Question 6. Answer: Explanation: Question 7. Question 8. Answer: Explanation: Question 9. Question 10. Answer: Explanation: In Exercises 11−14, write an equation in slope-intercept form of the line shown. Question 11. Answer: Question 12. Answer: Explanation: Question 13. Answer: Question 14. Answer: Explanation: In Exercises 15−20, write an equation in slope-intercept form of the line that passes through the given points. Question 15. Question 16. Answer: Explanation: Question 17. Question 18. Answer: Explanation: Question 19. Question 20. Answer: Explanation: In Exercises 21−26, write a linear function f with the given values. Question 21. Question 22. Answer: Explanation: Question 23. Question 24. Answer: Explanation: Question 25. Question 26. Answer: Explanation: In Exercises 27−30, tell whether the data in the table can be modeled by a linear equation. Explain. If possible, write a linear equation that represents y as a function of x. Question 27. Answer: Question 28. Answer: Explanation: Question 29. Answer: Question 30. Answer: Explanation: Question 31. Answer: Question 32. Answer: Question 33. Question 34. a. Can the situation be modeled by a linear equation? Explain. b. What is the processing fee? the daily fee? c. You can spend no more than $1200 on the beach house rental. What is the maximum number of days you can rent the beach house? Answer: Explanation: Question 35. Question 36. Answer: Explanation: Question 37. Question 38. a. Does the y-intercept of the graph of the linear function appear to be positive or negative? Explain. b. Estimate the coordinates of the two points. How can you use your estimates to confirm your answer in part (a)? Answer: Explanation: Question 39. Question 40. a. Which sibling received the most money? the least money? b. Which sibling spends money at the fastest rate? the slowest rate? c. Which sibling runs out of money first? last? Answer: Explanation: Maintaining Mathematical Proficiency Write the reciprocal of the number. Question 41. Question 42. Answer: Question
43. Question 44. Answer: Lesson 4.3 Writing Equations of Parallel and Perpendicular LinesEssential Equation EXPLORATION 1 EXPLORATION 2 Communicate Your Answer Question 3. Answer: Question 4. Answer: Question 5. Answer: 4.3 Lesson Question 1. Answer: Explanation: Question 2. Answer: Explanation: Monitoring Progress Question 3. Answer: Explanation: Question 4. Answer: Explanation: Question 5. Answer: Explanation: Writing Equations of Parallel and Perpendicular Lines 4.3 ExercisesVocabulary and Core Concept Check Question 1. Question 2. Answer: Monitoring Progress and Modeling with Mathematics In Exercises 3–8, determine which of the lines, if any, are parallel. Explain. Question 3. Answer: Question 4. Answer: Explanation: Question 5. Question 6. Answer: Explanation: Question 7. Question 8. Answer: Explanation: In Exercises 9–12, write an equation of the line that passes through the given point and is parallel to the given line. Question 9. Question 10. Answer: Explanation: Question 11. Question 12. Answer: Explanation: In Exercises 13–18, determine which of the lines, if any, are parallel or perpendicular. Explain. Question 13. Answer: Question 14. Answer: Explanation: Question 15. Question 16. Answer: Explanation: Question 17. Question 18. Answer: Explanation: In Exercises 19–22, write an equation of the line that passes through the given point and is perpendicular to the given line. Question 19. Question 20. Answer: Explanation: Question 21. Question 22. Answer: Explanation: In Exercises 23 and 24, write an equation of the line that passes through the given point and is (a) parallel and(b) perpendicular to the given line. Question 23. Answer: Question 24. Answer: Explanation: Question 25. Answer: Question 26. Answer: The perpendicular line slope is -3 y + 5 = -3(x – 4) y + 5 = -3x + 12 y = -3x + 12 – 5 y = -3x + 7 Question 27. Answer: Question 28. Answer: Explanation: Question 29. Question 30. Answer: Explanation: Question 31. Answer: Question 32. a. Did one of the students pay a greater registration fee? Explain. b. Did one of the students pay a greater monthly fee? Explain. Answer: a. From the graph we can say that Student B paid a greater registration fee. b. Yes, student B pay a greater monthly fee. REASONING Question 33. Question 34. Answer: Question 35. Question 36. Answer: Explanation: Maintaining Mathematical Proficiency Determine whether the relation is a function. Explain. (Section 3.1) Question 37. Question 38. Answer: Writing Linear Functions Study Skills: Getting Actively Involved in Class4.1–4.3 What Did You Learn Core Vocabulary Core Concepts Section 4.1 Section 4.2 Section 4.3 Mathematical Practices Question 1. Answer: Question
2. Answer: Question 3. Study Skills Getting Actively Involved in Class If you do not understand something at all and do not even know how to phrase a question, just ask for clarification. You might say something like, “Could you please explain the
steps in this problem one more time?”If your teacher asks for someone to go up to the board, volunteer. The student at the board often receives additional attention and instruction to complete the problem. Writing Linear Functions 4.1 – 4.34.1 – 4.3 Quiz Write an equation of the line in slope-intercept form. (Section 4.1) Question 1. Answer: Explanation: Question 2. Answer: Explanation: Question 3. Answer: Explanation: Write an equation in point-slope form of the line that passes through the given points. (Section 4.2) Question 4. Answer: Explanation: Question 5. Answer: Explanation: Question 6. Answer: Explanation: Write a linear function f with the given values. (Section 4.1 and Section 4.2) Question 7. Answer: Explanation: Question 8. Answer: Explanation: Question 9. Answer: Explanation: Determine which of the lines, if any, are parallel or perpendicular. Explain. (Section 4.3) Question 10. Answer: Explanation: Question 11. Answer: Explanation: Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line. (Section 4.3) Question 12. Answer: Explanation: Question 13. Answer: Explanation: Question 14. Answer: Explanation: Question 15. Answer: Explanation: Question 16. Answer: Explanation: Lesson 4.4 Scatter Plots and Lines of FitEssential Question How can you use a scatter plot and a line of fit to make conclusions about data? EXPLORATION 1 a. Draw a line that approximates the data. Write an equation of the line. Explain the method you used. b. What conclusions can you make from the equation you wrote? Explain your reasoning. EXPLORATION 2 b. What conclusions can you make from the equation you wrote? c. Use your equation to predict the median age of American women at their first marriage in the year 2020. Communicate Your Answer Question 3. Question 4. 4.4 Lesson Monitoring Progress Question 1. Answer: Question 2. Answer: Make a scatter plot of the data. Tell whether the data show a positive, a negative, or no correlation. Question 3. Answer: The number of attendees increases as the average temperature increases. So, the scatter plot shows a positive correlation. Question 4. Answer: As the age of car increases the value decreases. So, the scatter plot shows a negative correlation. Question 5. Scatter Plots and Lines of Fit 4.4 ExercisesQuestion 1. Question 2. Answer: Monitoring Progress and Modeling with Mathematics In Exercises 3–6, use the scatter plot to fill in the missing coordinate of the ordered pair. Question 3. Answer: Question 4. Answer: (3, 14) Question 5. Answer: Question 6. Answer: (8, 17) Question 7. a. What is the price of the laptop with a hard drive capacity of 8 gigabytes? b. What is the hard drive capacity of the $1200 laptop? c. What tends to happen to the price as the hard drive capacity increases? Answer: Question 8. a. What is the winning percentage of the pitcher with an earned run average of 4.2? b. What is the earned run average of the pitcher with a winning percentage of 0.33? c. What tends to happen to the winning percentage as the earned run average increases? Answer: In Exercises 9–12, tell whether x and y show a positive, a negative, or no correlation. Question 9. Answer: Question 10. Answer: Question 11. Answer: Question 12. Answer: In Exercises 13 and 14, make a scatter plot of the data. Tell whether x and y show a positive, a negative, or no correlation. Question 13. Answer: Question 14. Answer: Question 15. a. Write an equation that models the birthrate as a function of the number of years since 1960. b. Interpret the slope and y-intercept of the line of fit. Answer: Question 16. a. Write an equation that models the server’s earnings as a function of the number of hours the server works. b. Interpret the slope and y-intercept of the line of fit. Answer: Explanation: Question 17. Question 18. Answer: Question 19. Question 20. Answer:
Explanation: Question 21. Question 22. Answer: Question 23. Question 24. Answer: Explanation: Maintaining Mathematical Proficiency Evaluate the function when x = −3, 0, and 4. (Section 3.3) Question 25. Question 26. Answer: Explanation: Question 27. Question 28. Answer: Explanation: Lesson 4.5 Analyzing Lines of FitEssential Question EXPLORATION 1 b. Use the linear regression feature to find an equation of the line of best fit. You should obtain results such as those shown below. c. Write an equation of the line of best fit. Compare your result with the equation you obtained in Exploration 2 in Section 4.4. Communicate Your Answer Question 2. Question 3. The data set relates the number of chirps per second for striped ground crickets and the outside temperature in degrees Fahrenheit. Make a scatter plot of the data. Then find an equation of the line of best fit. Use your result to estimate the outside temperature when there are 19 chirps per second. Answer: Equation of the best fit line is y = 3.275x + 24.984 x = 19 in y = 3.275x + 24.984 y = 3.275(19) + 24.984 y = 62.225 + 24.984 y = 87.209 So, the outside temperature is 87.2°F when there are 19 chirps per second. 4.5 Lesson Monitoring Progress Question 1. Answer: Explanation:
The points are not evenly dispersed above the horizontal axis. So, the equation is y = -9.8x + 850 is not a good fit. Question 2. Answer: Explanation: Question 3. Answer: Explanation: Question 4. Analyzing Lines of Fit 4.5 ExercisesVocabulary and Core Concept Check Question 1. Question 2. Answer: Question 3. Question 4. Answer: Monitoring Progress and Modeling with Mathematics In Exercises 5–8, use residuals to determine whether the model is a good fit for the data in the table. Explain. Question 5. Answer: Question 6. Answer: Explanation:
The points are even;y dispersed about the horizontal axis. So the equation is a good fit. Question 7. Answer: Question 8. Answer: Explanation:
The points are evenly dispersed about the horizontal axis. So the equation is a good fit. Question 9. Answer: Question 10. Answer: Explanation:
Most of the residuals are below the horizontal axis. So, the equation does not model the data well. In Exercises 11–14, use a graphing calculator to find an equation of the line of best fit for the data. Identify and interpret the correlation coefficient. Question 11. Answer: Question 12. Answer: Question 13. Answer: Question 14. Answer: ERROR ANALYSIS Question 15. Answer: Question 16. Answer: Question 17. b. Identify and interpret the correlation coefficient. c. Interpret the slope and y-intercept of the line of best fit. Answer: Question 18. a. Use a graphing calculator to find an equation of the line of best fit. Then plot the data and graph the equation in the same viewing window. b. Identify and interpret the correlation coefficient. c. Interpret the slope and y-intercept of the line of best fit. Answer: The equation is y = -2x + 19 b. correlation coefficient is 0.6193. c. Slope is 1, y-intercept is 6.75. Question 19. a. Use a graphing calculator to find an equation of the line of best fit. b. Identify and interpret the correlation coefficient. c. Interpret the slope and y-intercept of the line of best fit. d. Approximate the mileage of an automobile that costs $15,500. e. Predict the price of an automobile with 6000 miles. Answer: Question 20. c. Interpret the slope and y-intercept of the line of best fit. d. Approximate the cost of a sailboat that is 20 feet long. e. Predict the length of a sailboat that costs $147,000. Answer: In Exercises 21–24, tell whether a correlation is likely in the situation. If so, tell whether there is a causal relationship. Explain your reasoning. Question 21. Question 22. Answer: Question 23. Question 24. Answer: Question 25. Question 26. Answer: a. The points appears to be linear and is having a positive slope. Thus the correlation coefficient of r = 0.98 matches the slope as it is very close to positive 1 showing a strong positive correlation. b. The points appears to be linear and is having a negative slope. Thus the correlation coefficient of r = -0.97 matches the slope as it is very close to -1 showing a strong negative correlation. c. The given graph shows scatter points. There is not a definite relationship between the two variables. Thus there is no correlation between them and therefore the correlation coefficient is r = 0. d. r = 0.69 as the slope in the graph is positive and somewhat linear and forms a graph of positive correlation as given in the question. Question 27. c. Another student watches about 14 hours of television each week. Approximate the student’s grade point average. d. Do you think there is a causal relationship between time spent watching television and grade point average? Explain. Answer: Question 28. Answer: Question 29. Answer: Question 30. Answer: Explanation:
These data were plotted on a coordinate axis system. A line was also graphed that fits the data function resulting Question 31. COMPARING METHODS The table shows the numbers y (in billions) of text messages sent each year in a five-year period, where x = 1 represents the first year in the five-year period. a. Use a graphing calculator to find an equation of the line of best fit. Identify and interpret the correlation coefficient. b. Is there a causal relationship? Explain your reasoning. c. Calculate the residuals. Then make a scatter plot of the residuals and interpret the results. d. Compare the methods you used in parts (a) and (c) to determine whether the model is a good fit. Which method do you prefer? Explain. Answer: Maintaining Mathematical Proficiency Determine whether the table represents a linear or nonlinear function. Explain. (Section 3.2) Question 32. Answer: Question 33. Answer: Lesson 4.6 Arithmetic SequencesEssential Question An arithmetic sequence is an ordered list of numbers in which the difference between each pair of consecutive terms, or numbers in the list, is the same. EXPLORATION 1 Communicate Your Answer Question 2. Question 3. 4.6 Lesson Monitoring Progress Write the next three terms of the arithmetic sequence. Question 1. Answer:
Add -12 to the term to find the next term. Question 2. Answer:
Add 0.4 to the term to get the next term. Question 3. Answer:
The next 3 terms are 3, 2(3/4), 2(1/2) Graph the arithmetic sequence. What do you notice? Question 4. Answer:
The points lie on the same line. Question 5. Answer:
The points lie on the same line Question 6. Answer:
The points lie on the same line. Question 7. Answer: Write an equation for the nth term of the arithmetic sequence. Then find a25. Question 8. Answer: Explanation: Question 9. Answer: Explanation: Question 10. Answer: Explanation: Question 11. Answer: c. You can play 12 games when you take $29 to the carnival. Explanation: Arithmetic Sequences 4.6 ExercisesVocabulary and Core Concept Check Question 1. Question 2. Answer: Monitoring Progress and Modeling with Mathematics In Exercises 3 and 4, write the next three terms of the arithmetic sequence. Question 3. Question 4. Answer:
The next 3 terms are 12, 6, 0. Question 5. Question 6. Answer: Question 7. Question 8. Answer: Question 9. Question 10. Answer: In Exercises 11−16, write the next three terms of the arithmetic sequence. Question 11. Question 12. Answer:
The next 3 terms are 46, 58, 70 Question 13. Question 14. Answer:
The next 3 terms are -60, -90, -120. Question 15. Question 16. Answer:
The next 3 terms are \(\frac{1}{6}\), 0, \(\frac{-1}{6}\) In Exercises 17−22, graph the arithmetic sequence. Question 17. Question 18. Answer:
Question 19. Question 20. Answer:
Question 21. Question 22. Answer:
In Exercises 23−26, determine whether the graph represents an arithmetic sequence. Explain. Question 23. Answer: Question 24. Answer: Explanation:
The consecutive terms have a common difference of 7. Question 25. Answer: Question 26. Answer: Explanation:
The consecutive terms do not have a common difference In Exercises 27−30, determine whether the sequence is arithmetic. If so, find the common difference. Question 27. Question 28. Answer:
The sequence is not arithmetic. Question 29. Question 30. Answer:
The sequence is arithmetic with a common difference of 6. Question 31. Answer: Question 32. Answer:
The consecutive terms do not have a common difference. In Exercises 33−38, write an equation for the nth term of the arithmetic sequence. Then find a10. Question 33. Question 34. Answer: Explanation: Question 35. Question 36. Answer: Explanation: Question 37. Question 38. Answer: Explanation: Question 39. Answer: Question 40. Answer: Question 41. Question 42. Answer: Explanation: REPEATED REASONING Question 43. Answer: Question 44. Answer: Question 45. a. Write a function that represents the arithmetic sequence. b. Graph the function. c. Estimate how many minutes after midnight January 1st it takes for 100 babies to be born. Answer: Question 46. a. Write a function that represents the arithmetic sequence. b. In what week does the movie earn $16 million? c. How much money does the movie earn overall? Answer: Explanation: MATHEMATICAL CONNECTIONS Question 47. Answer: Question 48. Answer:
The boxes do not represent the arithmetic sequence. Question 50. Answer: Question 51. THOUGHT PROVOKING Describe an arithmetic sequence that models the numbers of people in a real-life situation. Answer: Question 53. Question 54. a. Does the graph represent an arithmetic sequence? Explain. b. Explain how you would estimate the cost of a six-page advertisement in the magazine. Answer: Question 55. Answer: Question 56. Answer: Question 57. Maintaining
Mathematical ProficiencySolve the inequality. Graph the solution. (Section 2.2)Question 58. Answer: Question 59. Question 60. Answer: Question 61. Graph the function. Compare the graph to the graph of f(x) = | x |. Describe the domain and range. (Section 3.7) Question 62. Answer:
Question 63. Question 64. Question 65. Lesson 4.7 Piecewise FunctionsEssential Question How can you describe a function that is represented by more than on equation? EXPLORATION 1 b. What is the value of the function when x = 0? How can you tell? c. Write an equation that represents the values of the function when x ≤ 0. d. Write an equation that represents the values of the function when x > 0. e. Combine the results of parts (c) and (d) to write a single description of the function. EXPLORATION 2 Communicate Your Answer Question 3. Question 4. 4.7 Lesson Monitoring Progress Evaluate the function. Question 1. Answer: Question 2. Answer: Question 3. Answer: Question
4. Answer: Question 5. Answer: Question 6. Answer: Describe the domain and range. Question 7. Answer: Question 8. Answer: Write a piecewise function for the graph. Question 9. Answer: Question 10. Answer: Question 11. Answer: Explanation: Question 12. The reference beam originates at (3, 0) and reflects off a mirror at (5, 4). Answer: Piecewise Functions 4.7 ExercisesVocabulary and Core Concept Check Question 1. Question 2. Monitoring Progress and Modeling with MathematicsIn Exercises 3–12, evaluate the function. Question 3. Question 4. Answer: Question 5. Question 6. Answer: Question 7. Question 8. Answer: Question 9. Question 10. Answer: Question 11. Question 12. Answer: Question 13. How far do you travel in 4 hours? Answer: Question 14. Determine the total cost of ordering 26 shirts. Answer: c(x) = 15.80x + 20 c(26) = 15.80(26) + 20 = 430.8 In Exercises 15–20, graph the function. Describe the domain and range. Question 15. Answer: Question 16. Answer:
The domain is all real numbers and the range is y ≤ -3. Question 17. Answer: Question 18. Answer:
The domain is all real numbers and the range is y < 4 Question 19. Answer: Question 20. Answer:
The domain is all real numbers and the range is y < 2. Question 21. Answer: Question 22. Answer: The graph is wrong for the first statement. In Exercises 23–30, write a piecewise function for the graph. Question 23. Answer: Question 24. Answer: For x ≤ 0, y = -3 use the points (0, 3) and (1, 1) m = \(\frac { 1 – 3 }{ 1 – 0 } \) = -2 y – 1 = -2(x – 1) y – 1 = -2x + 2 y = -2x + 3, for x < 0 Question 25. Answer: Question 26. Answer: Use the points (-2, -2) and (2, 0) m = \(\frac { 0 + 2 }{ 2 + 2 } \) = \(\frac { 1 }{ 2 } \) The equation is y – 2 = \(\frac { 1 }{ 2 } \)(x – 0) y = \(\frac { 1 }{ 2 } \)x + 2 y = \(\frac { 1 }{ 2 } \)x + 2 for x > -2 Use the points (-2, -2) and (-4, -6) m = \(\frac { -6 + 2 }{ -4 + 2 } \) = 2 y + 2 = 2(x + 2) y = 2x + 2 for x < -2 Question 27. Answer: Question 28. Answer: Use the points (-1, 3), (-2, 2) m = \(\frac { 2 – 3 }{ -2 + 1 } \) = 1 y – 2 = 1(x + 2) y = x – 4 for x < -1 Use the points (-2, 0) and (3, -1) m = \(\frac { -1 – 0 }{ 3 + 2 } \) = \(\frac { -1 }{ 5 } \) y – 0 = \(\frac { -1 }{ 5 } \)(x + 2) y = \(\frac { -1 }{ 5 } \)(x + 2) for -2 > x < 3 y = -3 for x > 3 Question 29. Answer: Question 30. Answer: y = 1 for 4 < x < 3 y = 2 for 3 < x < 2 y = 3 for 2 < x < 1 y = 4 for 1 < x < 0 In Exercises 31–34, graph the step function. Describe the domain and range. Question
31. Answer: Question 32. Answer: Question 33. Answer: Question 34. Answer: Question 35. Question 36. Answer: f(x) = {4, if 0<x≤1 8, if 1<x≤2 12,if 2<x≤3 16,if 3<x≤4 In Exercises 37–46, write the absolute value function as a piecewise function. Question 37. Question 38. Answer: Question 39. Question 40. Answer: Question 41. Question 42. Answer: Question 43. Question 44. Answer: Question 45. Question 46. Answer: Question 47. a. Write an absolute value function that represents the path of the sunlight that reflects off the water. b. Write the function in part (a) as a piecewise function. Answer: Question 48. a. Write an absolute value function that represents the path of the golf ball. b. Write the function in part (a) as a piecewise function. Answer: Question 49. a. What is the value of f(-10)? b. What is the value of f(8)? Answer: Question 50. Answer: Question 51. Describe the domain and range. Answer: Question 52. a. Does it cost more money to make 100 photocopies or 101 photocopies? Explain. b. You have $40 to make photocopies. Can you buy more than 500 photocopies? Explain. Answer: Each piece of a function is linear C(x) = {0.15x, 0 < x ≤ 25, 0.10x, 25 < x ≤ 100, 0.07x, 100 < x ≤ 500, 0.05x, x > 500 Question 53. Answer: Question 54. does not represent a function. How can you redefine y so that it does represent a function? Answer: Question 55. Maintaining Mathematical ProficiencyWrite the sentence as an inequality. Graph the inequality.(Section 2.5) Question 56. Answer: Question 57. Question 58. Answer: Question 59. Question 60. Writing Linear Functions Performance Task: Any Beginning4.4–4.7 What Did You Learn? Core VocabularySection
4.4 Section 4.5 Section 4.6 Section 4.7 Mathematical Practices Question 1. Question 2. Question 3. Performance TaskAny Beginning To explore the answers to this question and more, go to Writing Linear Functions Chapter ReviewQuestion 1. Answer: Explanation: Question 2. Answer: Explnation: Write a linear function f with the given values. Question 3. Answer: Explanation: Question 4. Answer: Explanation: Question 5. Answer: Explanation: Question 6. Answer: Explanation: Question 7. Answer: Explanation: Question 8. Answer: Explanation: Question 9. Answer: Explanation: Question 10. Answer: Question 11. Answer: Question 12. Question 13. Answer: Question 14. write an equation for the nth term of the arithmetic sequence. Then find a30. Question 15. Answer: Explanation: Question 16. Answer: Explanation: Question 17. Answer: Explanation: Question 18. Answer: Explanation: Graph the function. Describe the domain and range. Question 19. Answer: Question 20. Answer: Write the absolute value function as a piecewise function. Question 21. Answer: Question 22. Answer: Question 23. Answer: Question 24. Answer: .Writing Linear Functions Chapter TestGraph the function. Describe the domain and range. Question 1. Question 2. Write an equation in slope-intercept form of the line with the given characteristics. Question 3. Answer: Question 4. Answer: Explanation: Question 5. Answer: Explanation: Question 6. Answer: Explanation: Write an equation in point-slope form of the line with the given characteristics. Question 7. Answer: Explanation: Question 8. Answer: Explanation: Question 9. Answer: Question 10. Answer: b. the points are (2000, 800) and (1500, 550) (y – 800) = \(\frac { 550 – 800 }{ 1500 – 2000 } \)(x – 2000) y – 800 = 0.5(x – 2000) y = 0.5x – 1000 + 800 y = 0.5x – 200 c. slope is 0.5 and y-intercept is -200. Question 11. Answer: Question 12. Answer: Explanation: Question 13. Answer: Writing Linear Functions Cumulative AssessmentQuestion 1. Answer: Question 2. Answer: Explanation: Question 3. Answer: Question 4. Answer: Question 5. Answer: Explanation: Question 6. Answer: Question 7. Answer: Question 8. Answer: Explanation: Question 9. a. Select the points that appear on a scatter plot of the residuals. b. Determine whether the model is a good fit for the data. Explain your reasoning. Answer:
(92, -6), (78, 96), (60, -10), (84, 58), (98, -64), (72, 94), (54, -72), (68, 26) The points are not above the x-axis. So the model does not fill well. |