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shelby1290

  • one year ago

A math textbook costs $60.00. The number of students who need the book is represented by x. The total cost of purchasing books for a group of students can be represented by the function f(x).

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  1. shelby1290
    • one year ago
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    a) Write an equation in function notation to represent the cost of purchasing textbooks for x students b) State the degree of this function and whether it is linear or quadratic c) Use your equation to calculate the cost of purchasing books for a class of 30 students d) What are the domain and range of this function, assuming that books can be purchased for two classes of students? Assume that the maximum number of students in a class is 30. Express your answers in set notation.

  2. hwyl
    • one year ago
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    OKAY LET US TRY

  3. hwyl
    • one year ago
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    IF YOU WANT TO BUY THIS BOOK, HOW MUCH WOULD YOU PAY?

  4. shelby1290
    • one year ago
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    @hwyl i wouldn't even buy it, i don't like math lol

  5. hwyl
    • one year ago
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    THIS IS JUST A HYPOTHETICAL QUESTION

  6. hwyl
    • one year ago
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    IF YOU WERE TO BUY A $60.00 BOOK, HOW MUCH WOULD YOU EXPECT TO PAY?

  7. shelby1290
    • one year ago
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    $60.00

  8. hwyl
    • one year ago
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    GOOD SO LET US CREATE A TABLE

  9. hwyl
    • one year ago
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    |dw:1442095256587:dw|

  10. hwyl
    • one year ago
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    let us say you and your friend wanted to buy the book, how much you two pay?

  11. hwyl
    • one year ago
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    buy the book for each of you to own

  12. hwyl
    • one year ago
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    make sense

  13. hwyl
    • one year ago
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    let us update our table

  14. shelby1290
    • one year ago
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    $120.00

  15. hwyl
    • one year ago
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    |dw:1442095394341:dw|

  16. hwyl
    • one year ago
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    let us say that 20 students needed to buy the book, how much would it sum to?

  17. shelby1290
    • one year ago
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    $1,200

  18. hwyl
    • one year ago
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    cool! so how about you update our table

  19. shelby1290
    • one year ago
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    what do i plug in for the x-values?

  20. hwyl
    • one year ago
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    |dw:1442095582413:dw|

  21. hwyl
    • one year ago
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    IT IS JUST AN EXAMPLE AND I AM USING YOU AS AN EXAMPLE IT DOES NOT MEAN THAT YOU WILL BUY THE BOOK FOR REAL

  22. hwyl
    • one year ago
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    DO YOU NOW FIGURE OUT HOW TO CREATE FUNCTIONS?

  23. shelby1290
    • one year ago
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    |dw:1442095906271:dw|

  24. shelby1290
    • one year ago
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    What do you mean by " do i now know how to create functions?"

  25. shelby1290
    • one year ago
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    And can you please stop typing in all capital letters?

  26. hwyl
    • one year ago
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    what do I mean, I mean do you now know how to write functions to be able to figure out your question letter A

  27. hwyl
    • one year ago
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    i like CAPS

  28. shelby1290
    • one year ago
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    Oh okay then no i don't know how to write an equation in function notation for part a)

  29. shelby1290
    • one year ago
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    @hwyl ^

  30. hwyl
    • one year ago
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    I put it in box lol

  31. shelby1290
    • one year ago
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    But how do I create an EQUATION ?

  32. kohai
    • one year ago
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    Okay, so you were on the right track

  33. kohai
    • one year ago
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    In this case, the function itself (a) is f(x) = 60x. You had that down. See where I pulled that from? (trying to get a baseline here)

  34. kohai
    • one year ago
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    Do you understand why that is the equation?

  35. shelby1290
    • one year ago
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    yes because 60 is the cost for the textbook

  36. kohai
    • one year ago
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    Right, 60 is the base number. So x represents a variable, meaning, you can plug any number into it. I'll show you so you can visibly see it

  37. kohai
    • one year ago
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    60*1 = 60 when x=1 6-*2 = 120 when x=2 etc. You can plug any number in there and multiply it and it'll be correct

  38. kohai
    • one year ago
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    So you've already done part A. f(x) = 60x

  39. kohai
    • one year ago
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    Do you know what kind of graph this would be? Linear vs quadratic?

  40. shelby1290
    • one year ago
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    linear because it has a degree of 1?

  41. kohai
    • one year ago
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    Very good, very good. You just did part b :) So it would be a straight line

  42. kohai
    • one year ago
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    So if you wanted to see how much it would cost to buy 30 books, do you know what you would do?

  43. shelby1290
    • one year ago
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    f(30)=60(30) = $1,800

  44. kohai
    • one year ago
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    You even have proper notation, nice. See, you're doing just fine :)

  45. kohai
    • one year ago
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    Now, what do you know about domain and range

  46. shelby1290
    • one year ago
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    Domain is {XER} and range is {YER}

  47. shelby1290
    • one year ago
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    I don't really understand how to set them up when i have a bunch of numbers.

  48. kohai
    • one year ago
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    I think you're better with algebra 1 than I was when I went through the course, I sucked at it. Yes. So basically domain is the x-values and range is the y-values. Do you want to take a wack at part d?

  49. shelby1290
    • one year ago
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    I know that i'll need greater and less than signs but idk where to place them

  50. shelby1290
    • one year ago
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    nooo don't say that lol i'm terrible at math. that's why im here asking a billion questions

  51. kohai
    • one year ago
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    Nothing wrong with asking questions, at all. But I've seen people 10x worse than you. You get it, you just have to be kinda guided in the right direction. Trust me, I know people who are terrible at math

  52. kohai
    • one year ago
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    So, take a look at the x-values. You know that the maximum there can be is 30 students, but that includes the 30th student.

  53. kohai
    • one year ago
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    So that means there will be an "-or equal to" in there

  54. kohai
    • one year ago
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    So think about it, will it be "greater than or equal to" 30 students, or "less than or equal to" 30 students?

  55. shelby1290
    • one year ago
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    I'm one of them haha and what you said is true. I do need extra help.

  56. shelby1290
    • one year ago
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    |dw:1442098912668:dw|

  57. shelby1290
    • one year ago
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    I'm not sure

  58. kohai
    • one year ago
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    Well I mean, you can't have greater than 30 students if 30 is the maximum right? You'd have to have less than or equal to 30 students?

  59. kohai
    • one year ago
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    You know what I mean?

  60. shelby1290
    • one year ago
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    so all i'm changing is the greater than signs to less thans ?

  61. kohai
    • one year ago
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    Yeah. You can have any number of students, as long as they're either exactly 30 or less than 30. You can't go over that. So it's less than or equal to

  62. kohai
    • one year ago
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    So the notation that's generally used for that is

  63. kohai
    • one year ago
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    \[x \le 30\]

  64. kohai
    • one year ago
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    That says that x is less than or equal to 30

  65. shelby1290
    • one year ago
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    ah okay so..|dw:1442099289067:dw|

  66. kohai
    • one year ago
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    Yeah exactly. If your teacher wants you to use the {XER|} that's fine. Most don't care and you can just put it plainly

  67. shelby1290
    • one year ago
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    what does it mean when you have two numbers inside of the brackets like i did before?

  68. kohai
    • one year ago
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    Can you show me an example?

  69. shelby1290
    • one year ago
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    i think im getting the differences mixed up

  70. kohai
    • one year ago
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    Oh, I see, okay. So when you have like, 0<x<30, it means that it can't be less than 0 or greater than 30

  71. kohai
    • one year ago
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    So for the purposes of this example, yeah, add that in

  72. kohai
    • one year ago
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    |dw:1442099479057:dw|

  73. kohai
    • one year ago
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    Glad you pointed that out :)

  74. shelby1290
    • one year ago
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    |dw:1442099423813:dw|

  75. shelby1290
    • one year ago
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    Like that or something ^

  76. shelby1290
    • one year ago
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    yes

  77. kohai
    • one year ago
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    So you understand what that means now yeah? And why it should be included?

  78. shelby1290
    • one year ago
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    like the way domains are set up?

  79. kohai
    • one year ago
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    Yeah, that

  80. kohai
    • one year ago
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    And why you should do 0<x<30 and not just x<30

  81. shelby1290
    • one year ago
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    Because you haven't bought the textbook yet so you start with 0? I don't know

  82. kohai
    • one year ago
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    Because the lowest number of students you can possibly have is 0. You can't have negative people :) The x-axis is the students in this case

  83. kohai
    • one year ago
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    If we had just x<30, it would mean any number less than 30. That means you could have like -600 students, theoretically

  84. shelby1290
    • one year ago
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    ahh okay i see. does the same thing go for the range?

  85. shelby1290
    • one year ago
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    {YER|0<y<30}

  86. kohai
    • one year ago
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    Kind of. You have the right idea

  87. kohai
    • one year ago
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    So in the range's case, it's all the y-values. So the y-values is the amount paid for textbooks

  88. kohai
    • one year ago
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    So what's the lowest value you can pay for a textbook?

  89. kohai
    • one year ago
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    (Not a trick question)

  90. shelby1290
    • one year ago
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    0

  91. kohai
    • one year ago
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    Yes, good

  92. kohai
    • one year ago
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    So, what is the highest amount you will pay if you have a maximum of 30 students?

  93. shelby1290
    • one year ago
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    30

  94. kohai
    • one year ago
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    You have 30 students. If 30 students pay $60 each, how much will all the textbooks cost? But you're right that 30 has to go into the equation

  95. shelby1290
    • one year ago
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    $1,800

  96. kohai
    • one year ago
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    Yup! So what's the range going to be?

  97. shelby1290
    • one year ago
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    {YER| 30>y>1800}

  98. kohai
    • one year ago
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    Close

  99. kohai
    • one year ago
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    30 has exclusively to do with x, so it's not going to be in there. Let me show you

  100. shelby1290
    • one year ago
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    okay

  101. kohai
    • one year ago
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    Oh, well, I guess so. I mean, it depends. You can have 0 students but I guess it's more likely your teacher would want at least one student rofl

  102. kohai
    • one year ago
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    So lemme fix it ;-;

  103. kohai
    • one year ago
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    |dw:1442100303626:dw|

  104. kohai
    • one year ago
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    I was thinking about it like apples. Lol. You can have 0 apples, but not a negative apple. Anyways

  105. kohai
    • one year ago
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    If you have one student, the maximum you'd pay is $60 for one textbook right?

  106. shelby1290
    • one year ago
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    yes that's true so is it correct even if i write down 0?

  107. kohai
    • one year ago
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    If you write down 0, no textbooks are being bought so the lowest you'd have is $0. So you can have one of these two things here

  108. kohai
    • one year ago
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    |dw:1442100443760:dw|

  109. kohai
    • one year ago
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    or

  110. kohai
    • one year ago
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    |dw:1442100503454:dw|

  111. kohai
    • one year ago
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    Does that make sense?

  112. shelby1290
    • one year ago
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    Yes, I get it now. Thank you so much!

  113. kohai
    • one year ago
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    You're welcome :) I hope I helped. Sorry for the mixup v,v

  114. shelby1290
    • one year ago
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    That's totally fine. As long as your explanations make sense! (which they did)

  115. shelby1290
    • one year ago
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    thanks again

  116. hwyl
    • one year ago
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    set notation is the easiest part of functions http://www.mathsisfun.com/sets/set-builder-notation.html

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