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Should We Buy a Laser Printer?

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Presentation on theme: "Should We Buy a Laser Printer?"— Presentation transcript:

0 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 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

1 Should We Buy a Laser Printer?
Linear Functions 1/16/13 Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

2 Comparison Shopping What could you shop for by price? HOOK
You could change the problem if there is a strong interest in the class for something else. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

3 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? HOOK Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

4 What does it mean to “represent” a function?
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 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

5 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 TASK Would the laser printer cost less than $0.014? Prices are rounded to the nearest $5. Let students decided whether they should choose the high yield toner cartridge. Practice1 Make sense of problems and persevere in solving them. F‐BF.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

6 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. Practice 3 Construct viable arguments and critique the reasoning of others. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

7 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 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

8 Laser vs. Inkjet Printers
The graph shows the estimated cost of buying and using an inkjet printer. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

9 Laser vs. Inkjet Printers
The estimated cost of buying and using a home laser printer can be found with the equation L(x) = x 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. # Attend to precision F‐IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F‐IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative. A‐REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). #2 1 Make sense of problems and persevere in solving them. A.REI.6 (NOT IN SCOPE AND SEQUENCE) Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. F-­IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). #3 1 Make sense of problems and persevere in solving them. F‐IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

10 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 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

11 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) = b) d(x) = 5.00d c) (x) = 7. Write a function to find the number of pages printed, p(x), as a function of the cost, x. p(x) = ____________________________ Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

12 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 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

13 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 domain range d(x) p(x) Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

14 Laser Printer Function of Pages
As you already found the estimated cost as a function of the number of pages printed is L(x) = x 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 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

15 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 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

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 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

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 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

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 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

19 Laser Printer Function of Pages
Find the value of x where L(x) = N(x). Describe the domain and range of each function. domain range d(x) p(x) Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

20 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 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

21 Learning Targets Linear Functions 3a:
I can identify the characteristics of linear functions and use function notation. 21 Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

22 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. 4 Model with mathematics. F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.  a Graph linear and quadratic functions and show intercepts, maxima, and minima. [Linear functions only] F-­BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [Linear functions only] Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

23 Printer Speeds inkjet printer laser printer Pages Time (sec) 4 54 6 70
10 102 18 166 4 Model with mathematics. F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.  a Graph linear and quadratic functions and show intercepts, maxima, and minima. [Linear functions only] F-­BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [Linear functions only] 23 Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License.  23

24 Be Prepared to Present Your Solution
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 3 Construct viable arguments and critique the reasoning of others. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

25 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)? You might want to use technology to show this graph. is what I used to make this graph. 4 Model with mathematics. F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.  a Graph linear and quadratic functions and show intercepts, maxima, and minima. [Linear functions only] F-­BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [Linear functions only] Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

26 Be Prepared to Present Your Solution
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 3 Construct viable arguments and critique the reasoning of others. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

27 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 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

28 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) = 17. Write a function to find the number of pages printed, p(x), as a function of the cost, x. #14 4 Model with mathematics. F-­LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-­output pairs (include reading these from a table).[Linear functions only] #15 & 16 1 Make sense of problems and persevere in solving them. F‐IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

29 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. #17 4 Model with mathematics. F-­BF.4  Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. #18 1 Make sense of problems and persevere in solving them. F‐IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. #19 1 Make sense of problems and persevere in solving them. F-­LE.1  Distinguish between situations that can be modeled with linear functions and with exponential functions. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

30 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 #20 1 Make sense of problems and persevere in solving them. A.REI.6 (NOT IN SCOPE AND SEQUENCE) Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables #21 4 Model with mathematics. F‐IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. 3 Construct viable arguments and critique the reasoning of others. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

31 Laser Printer Function of Pages
As you already found the estimated cost as a function of the number of pages printed is L(x) = x 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 4 Model with mathematics. F‐IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F‐IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

32 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. 4 Model with mathematics. #24 A-CED.4 (Not in Scope & Sequence) Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.  #25 & 26 F‐IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

33 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. #27 1 Make sense of problems and persevere in solving them F-­LE.1  Distinguish between situations that can be modeled with linear functions and with exponential functions. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. #28 4 Model with mathematics. A.REI.6 (NOT IN SCOPE AND SEQUENCE) Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables #29 1 Make sense of problems and persevere in solving them F‐IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

34 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 4 Model with mathematics. F-­BF.4  Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2x3 or f(x) = (x + 1)/(x -­ 1) for x ≠ 1. [Linear functions only] 3 Construct viable arguments and critique the reasoning of others. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

35 Learning Target LF3a I can identify the characteristics of linear functions and use function notation. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

36 Be Prepared to Present Your Solution
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 # Attend to precision. F-­IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). A‐REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). #33 4 Model with mathematics. F-­LE.1  Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

37 Learning Target LF3a I can identify the characteristics of linear functions and use function notation. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

38 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 $ Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

39 Be Prepared to Present Your Solution
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 #34 4 Model with mathematics. F‐BF.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context. #35 4 Model with mathematics. F-­LE.1  Distinguish between situations that can be modeled with linear functions and with exponential functions. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another #36 4 Model with mathematics. A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. # Make sense of problems and persevere in solving them. F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.  a Graph linear and quadratic functions and show intercepts, maxima, and minima. 3 Construct viable arguments and critique the reasoning of others. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

40 Learning Target LF3a I can identify the characteristics of linear functions and use function notation. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

41 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 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

42 Laser Printer Detailed Costs
Throughout this lesson, we have used the function L(x) = x to estimate the printer costs. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

43 Laser Printer Detailed Costs
Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

44 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? 1 Make sense of problems and persevere in solving them. #38 F‐IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). #39 F-­LE.1  Distinguish between situations that can be modeled with linear functions Prove that linear functions grow by equal differences over equal intervals; #40 F‐IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. #41 F‐IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. F-­IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. [Linear functions only] Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

45 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 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

46 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? The costs of toner, drum and paper are the same for both printers. Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

47 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? OPTIONAL: If you choose to do this, move it to after the presentations 6 Attend to precision. communicate precisely to others are careful about specifying units of measure calculate accurately and efficiently express numerical answers with a degree of precision appropriate for the problem context Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 

48 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 6 Attend to precision. communicate precisely to others are careful about specifying units of measure calculate accurately and efficiently express numerical answers with a degree of precision appropriate for the problem context Algebra 1 by Southwest Washington Common Core Mathematics is licensed under a Creative Commons Attribution 4.0 International License. 


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