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Teacher Notes. You might want to update prices at Office Max PRACTICES: 1 Problem solving & perseverance, 3 Construct viable arguments and critique the reasoning of others, 4 Model with mathematics, 6 Attend to precision.

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Teacher Notes

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  1. Teacher Notes You might want to update prices at Office Max PRACTICES: 1 Problem solving & perseverance, 3 Construct viable arguments and critique the reasoning of others, 4 Model with mathematics, 6 Attend to precision. The slides for DUPLEX laser printer and Precision at the end of the presentation are optional. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  2. Should We Buy a Laser Printer? Linear Functions Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  3. Comparison Shopping • What could you shop for by price? Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  4. Should We Buy a Laser Printer? • The least expensive way to make copies is through the district Print Shop. • They charge us $0.014 for one single-sided black and white copy. • Would it cost the math department less money for one single sided copy if we bought a black and white laser printer? Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  5. Learning Target Linear Function 2a I can represent a situation using tables, graphs, equations and in words. What does it mean to “represent” a function? Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  6. Should We Buy a Laser Printer? Need 1 of toner cartridge High Yield Black Toner Cartridge • Yields up to 2,600 pages • Price: $70 Black Toner Cartridge • Yields up to 1,200 pages • Price: $45 Need both Drum Cartridge • Yields up to 12,000 page • Price: $105 Multipurpose Paper • 5,000/Case • Price:$50 Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  7. Present Your Solution to the Class • Mr. Benson manages the district Print Shop. • Write a letter to Mr. Benson to convince him to whether or not to buy the math department laser printers. • Support your answer with mathematical information in your letter. • Listen to the presentations of others. • - Write one complement about their mathematics. • - Write one question about their mathematics. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  8. Learning Targets LF2b I can identify a function and its domain and range, and use function notation to find quantities in the domain or range. LF3a I can identify the characteristics of linear functions and use function notation. LF3b I can write equations of linear functions and linear functions them to solve problems. LF4 I can find when a point where two equations have the same solution. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  9. Laser vs. Inkjet Printers The graph shows the estimated cost of buying and using an inkjet printer. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  10. Laser vs. Inkjet Printers The estimated cost of buying and using a home laser printer can be found with the equation L(x) = 0.04567x + 110 where x is the number of pages. • Use the graph to decide whether it is more cost effective to use the laser printer or the school copier for 10, 100, 1000 or 5000 copies. • How many pages do you need to print for the laser printer to be more cost effective? • Describe the domain and range of each function. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  11. Learning Target • LF2b I can identify a function and its domain and range, and use function notation to find quantities in the domain or range. • LF3c I can compare two functions or one function represented two different ways. • Find the inverse function • LF4 I can solve a system of equations with a table or by graphing. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  12. Laser Printer Function of Pages The district Print Shop charges $0.014for single-sided white paper. • Write the equation for The Print Shop costs are determined by the function, where the cost, d(x), is a function of the number of pages printed, x. • Use your equation to find: a) Find d(10) b) Find d(150) C) Find d(800) • Use your equation to solve for x. a) d(x) = 1.00 b) d(x) = 5.00d c)(x) = 100.00 7. Write a function to find the number of pages printed, p(x), as a function of the cost, x. p(x) = ____________________________ Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  13. Laser Printer Function of Pages The function p(x) is the inverse function of d(x), because they undo each other. In other words, when d(a) = b, then p(b) = a. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  14. Laser Printer Function of Pages • Use p(x) = to verify your answers to #16. • Is the function, p(x), linear? Support your answer with words, numbers and/or diagrams. • Find the value of x where d(x) = p(x). • Describe the domain and range of each function. Be Prepared to Present Your Solution to the Class Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  15. Laser Printer Function of Pages As you already found the estimated cost as a function of the number of pages printed is L(x) = 0.04567x + 110 . • For L(x), _____________ is the input and ________________ is the out put. • Use your equation to solve for x. • L(x) = 110 • L(x) = 150 • L(x) = 10 Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  16. Laser Printer Function of Pages • Now find N(x), the inverse function of L(x). • For N(x), For L(x), _____________ is the input and ________________ is the out put. • Use p(x) = to verify your answers to #23. • Is the function, N(x), linear? Support your answer with words, numbers and/or diagrams. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  17. Laser Printer Function of Pages • Now find N(x), the inverse function of L(x). • For N(x), For L(x), _____________ is the input and ________________ is the out put. • Use p(x) = to verify your answers to #23. • Is the function, N(x), linear? Support your answer with words, numbers and/or diagrams. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  18. Laser Printer Function of Pages • Now find N(x), the inverse function of L(x). • For N(x), For L(x), _____________ is the input and ________________ is the out put. • Use p(x) = to verify your answers to #23. • Is the function, N(x), linear? Support your answer with words, numbers and/or diagrams. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  19. Laser Printer Function of Pages • Now find N(x), the inverse function of L(x). • For N(x), For L(x), _____________ is the input and ________________ is the out put. • Use p(x) = to verify your answers to #23. • Is the function, N(x), linear? Support your answer with words, numbers and/or diagrams. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  20. Laser Printer Function of Pages • Find the value of x where L(x) = N(x). • Describe the domain and range of each function. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  21. Laser Printer Function of Pages • In #18 and #23, you were asked to find the value of x where the function and its inverse function were equal to each other. What do your answers to #18 and #23 have in common? • In #19 and #24, you were asked to find the domain and range of function and its inverse function. What do your answers to #19 and #24 have in common? Be Prepared to Present Your Solution to the Class Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  22. Learning Targets Linear Functions 3a: I can identify the characteristics of linear functions and use function notation. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015 21

  23. Printer Speeds Mr. Aho wants to know if the laser printer is faster than the inkjet printer he already has. He used his inkjet printer to print pages and recorded the pages and times in the table. He looked up the specifications for the laser printer he wants to buy and made a graph to determine the time it would take to print pages. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  24. Printer Speeds Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015 23

  25. Price Changes 1 • Describe the input and output of the laser printer function, L(x). • Was the input or the output changed in #5? Support your answer with words, numbers and/or diagrams. • Was the input or the output changed in #6? Support your answer with words, numbers and/or diagrams. Be Prepared to Present Your Solution Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  26. Price Changes 2 • Mr. Blake liked Mrs. Krsak’s idea of buying a laser printer and decided to buy a laser printer for his home at the beginning of second semester. He has one Algebra 1 class fall semester, and three Algebra 1 classes next semester. How does this change the graph of the function L(x)? • Mrs. Doss also decided to buy a laser printer for her home at the beginning of second semester. Mrs. Doss’s schedule is changing also. She has 70 fewer students in Algebra 1 classes next semester because she’s teaching more Geometry classes. How does this change the graph of the function L(x)? Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  27. Price Changes 2 11. Describe the input and output of the laser printer function, L(x). 12. Was the input or the output changed in #9? Support your answer with words, numbers and/or diagrams. 13. Was the input or the output changed in #10? Support your answer with words, numbers and/or diagrams. Be Prepared to Present Your Solution Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  28. Learning Targets LF2b I can identify a function and its domain and range, and use function notation to find quantities in the domain or range. LF3c I can compare two functions or one function represented two different ways. Find the inverse function LF4 I can solve a system of equations with a table or by graphing. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  29. Laser Printer Function of Pages The district Print Shop charges $0.014for single-sided white paper. 14. Write the equation for The Print Shop costs are determined by the function, where the cost, d(x), is a function of the number of pages printed, x. 15. Use your equation to find d(10), d(150), and d(800) 16. Use your equation to solve for x: d(x) = 1.00, d(x) = 5.00, and d(x) = 100.00 17. Write a function to find the number of pages printed, p(x), as a function of the cost, x. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  30. Laser Printer Function of Pages The function p(x) is the inverse function of d(x), because they undo each other. In other words, when d(a) = b, then p(b) = a. 18. Use p(x) = to verify your answers to #16. 19. Is the function, p(x), linear? • Support your answer with words, numbers and/or diagrams. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  31. Laser Printer Function of Pages • Find the value of x where d(x) = p(x). • Describe the domain and range of each function. Be Prepared to Present Your Solution Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  32. Laser Printer Function of Pages As you already found the estimated cost as a function of the number of pages printed is L(x) = 0.04567x + 110 . 22. For L(x), _______ is the input and _______ is the out put. 23. Use your equation to solve for x. • L(x) = 110 • L(x) = 150 • L(x) = 10 Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  33. Laser Printer Function of Pages 24. Now find N(x), the inverse function of L(x). 25. For N(x), _______ is the input and _______ is the out put. 26. Use p(x) = to verify your answers to #23. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  34. Laser Printer Function of Pages 27. Is the function, N(x), linear? • Support your answer with words, numbers and/or diagrams. • Find the value of x where L(x) = N(x). • Describe the domain and range of each function. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  35. Laser Printer Function of Pages 30. In #18 and #23, you were asked to find the value of x where the function and its inverse function were equal to each other. What do your answers to #18 and #23 have in common? • In #19 and #24, you were asked to find the domain and range of function and its inverse function. What do your answers to #19 and #24 have in common? Be Prepared to Present Your Solution Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  36. Learning Target LF3a I can identify the characteristics of linear functions and use function notation. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  37. Printer Speeds Mr. Aho wants to know if the laser printer is faster than the inkjet printer he already has. He used his inkjet printer to print pages and recorded the pages and times in the table. He looked up the specifications for the laser printer he wants to buy and made a graph to determine the time it would take to print pages. • Use the laser printer table and the inkjet printer graph to answer Mr. Aho’s question. • Is Mr. Aho’s inkjet printer function, represented by a table, linear? Support your answer with words, numbers and/or diagrams. Be Prepared to Present Your Solution Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  38. Learning Target LF3a I can identify the characteristics of linear functions and use function notation. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  39. Printing Budget The school district is trying to save money. They put all teachers on a $900 budget for what they order from the Print Shop. At the end of first semester Mr. Kaden had ordered 48,963 copies (both one-sided and two-sided, and white and color paper) from the Print Shop and was charged $485.14. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  40. Printing Budget 34. Write a function Mr. Kaden can use to determine what is left in his budget from the number of copies he has made. Be sure to define the variables you use. • Is the budget function linear? Support your answer with words, numbers and/or diagrams. 36. Make a graph that Mr. Kaden can refer to and find out how much of his budget remains. Be sure to show in your graph when Mr. Kaden has no money left in his budget. 37. Find the maximum number of copies Mr. Kaden can make. Support your answer with information from your graph. Be Prepared to Present Your Solution Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  41. Learning Target LF3a I can identify the characteristics of linear functions and use function notation. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  42. Laser Printer Detailed Costs If we buy paper, toner and drum cartridges, as we need them would the graph really look like this? • If you think this is the graph, support your answer with words, numbers and/or diagrams. • If you think the graph would be different, describe or sketch the new graph. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  43. Laser Printer Detailed Costs Throughout this lesson, we have used the function L(x) = 0.04567x + 110 to estimate the printer costs. Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  44. Laser Printer Detailed Costs Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  45. Laser Printer Detailed Costs Mr. Aho made a detailed graph of the costs of the laser printer. Support all of your answers with information from the diagram. • Is the graph a function? • Is the graph a linear function? • Describe the domain and range of the values shown on the graph. • Find the start up cost of the printer. What is included in that cost? Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  46. Laser Printer Detailed Costs Support all of your answers with information from the diagram. 38. Is the graph a function? 39. Is the graph a linear function? 40. Describe the domain and range of the values shown on the graph. 41. Find the start up cost of the printer. What is included in that cost? 42. Pick two different intervals. Describe what is happening in each of the intervals. Be Prepared to Present Your Solution Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  47. Should We Buy a Duplex Laser Printer? • The least expensive way to make copies is through the district Print Shop. • They charge us $0.02 for one single-sided black and white copy. • Would it cost the math department less money for one single sided copy if we bought a black and white laser printer? Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  48. Precision • How many decimal places did you use when you calculated the cost of toner for 1 page? LIST ANSWERS: • How many places are necessary? • How can you find a more accurate answer? Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

  49. Precision HOW TO USE THE MEMORY OF A GRAPHING CALCULATOR • Find cost of toner for 1 page. Store this cost in your calculator as “T” STO> T • Find cost of the drum for 1 page. Store this cost in your calculator as “D” STO> D • Find cost of 1 piece of paper. Store this cost in your calculator as “P” • The cost of 1 page T + D + P • Find cost of toner for 1 page. Store this cost in your calculator as “T” STO> C Algebra 1bySouthwest Washington Common Core Mathematicsis licensed under a Creative Commons Attribution 4.0 International License.  2014-2015

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