## 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).

1. shelby1290

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

OKAY LET US TRY

3. hwyl

IF YOU WANT TO BUY THIS BOOK, HOW MUCH WOULD YOU PAY?

4. shelby1290

@hwyl i wouldn't even buy it, i don't like math lol

5. hwyl

THIS IS JUST A HYPOTHETICAL QUESTION

6. hwyl

IF YOU WERE TO BUY A \$60.00 BOOK, HOW MUCH WOULD YOU EXPECT TO PAY?

7. shelby1290

\$60.00

8. hwyl

GOOD SO LET US CREATE A TABLE

9. hwyl

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10. hwyl

let us say you and your friend wanted to buy the book, how much you two pay?

11. hwyl

buy the book for each of you to own

12. hwyl

make sense

13. hwyl

let us update our table

14. shelby1290

\$120.00

15. hwyl

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16. hwyl

let us say that 20 students needed to buy the book, how much would it sum to?

17. shelby1290

\$1,200

18. hwyl

cool! so how about you update our table

19. shelby1290

what do i plug in for the x-values?

20. hwyl

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21. hwyl

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

DO YOU NOW FIGURE OUT HOW TO CREATE FUNCTIONS?

23. shelby1290

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24. shelby1290

What do you mean by " do i now know how to create functions?"

25. shelby1290

And can you please stop typing in all capital letters?

26. hwyl

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

i like CAPS

28. shelby1290

Oh okay then no i don't know how to write an equation in function notation for part a)

29. shelby1290

@hwyl ^

30. hwyl

I put it in box lol

31. shelby1290

But how do I create an EQUATION ?

32. kohai

Okay, so you were on the right track

33. kohai

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

Do you understand why that is the equation?

35. shelby1290

yes because 60 is the cost for the textbook

36. kohai

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

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

So you've already done part A. f(x) = 60x

39. kohai

Do you know what kind of graph this would be? Linear vs quadratic?

40. shelby1290

linear because it has a degree of 1?

41. kohai

Very good, very good. You just did part b :) So it would be a straight line

42. kohai

So if you wanted to see how much it would cost to buy 30 books, do you know what you would do?

43. shelby1290

f(30)=60(30) = \$1,800

44. kohai

You even have proper notation, nice. See, you're doing just fine :)

45. kohai

Now, what do you know about domain and range

46. shelby1290

Domain is {XER} and range is {YER}

47. shelby1290

I don't really understand how to set them up when i have a bunch of numbers.

48. kohai

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

I know that i'll need greater and less than signs but idk where to place them

50. shelby1290

nooo don't say that lol i'm terrible at math. that's why im here asking a billion questions

51. kohai

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

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

So that means there will be an "-or equal to" in there

54. kohai

So think about it, will it be "greater than or equal to" 30 students, or "less than or equal to" 30 students?

55. shelby1290

I'm one of them haha and what you said is true. I do need extra help.

56. shelby1290

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57. shelby1290

I'm not sure

58. kohai

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

You know what I mean?

60. shelby1290

so all i'm changing is the greater than signs to less thans ?

61. kohai

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

So the notation that's generally used for that is

63. kohai

\[x \le 30\]

64. kohai

That says that x is less than or equal to 30

65. shelby1290

ah okay so..|dw:1442099289067:dw|

66. kohai

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

what does it mean when you have two numbers inside of the brackets like i did before?

68. kohai

Can you show me an example?

69. shelby1290

i think im getting the differences mixed up

70. kohai

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

So for the purposes of this example, yeah, add that in

72. kohai

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73. kohai

Glad you pointed that out :)

74. shelby1290

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75. shelby1290

Like that or something ^

76. shelby1290

yes

77. kohai

So you understand what that means now yeah? And why it should be included?

78. shelby1290

like the way domains are set up?

79. kohai

Yeah, that

80. kohai

And why you should do 0<x<30 and not just x<30

81. shelby1290

Because you haven't bought the textbook yet so you start with 0? I don't know

82. kohai

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

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

ahh okay i see. does the same thing go for the range?

85. shelby1290

{YER|0<y<30}

86. kohai

Kind of. You have the right idea

87. kohai

So in the range's case, it's all the y-values. So the y-values is the amount paid for textbooks

88. kohai

So what's the lowest value you can pay for a textbook?

89. kohai

(Not a trick question)

90. shelby1290

0

91. kohai

Yes, good

92. kohai

So, what is the highest amount you will pay if you have a maximum of 30 students?

93. shelby1290

30

94. kohai

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

\$1,800

96. kohai

Yup! So what's the range going to be?

97. shelby1290

{YER| 30>y>1800}

98. kohai

Close

99. kohai

30 has exclusively to do with x, so it's not going to be in there. Let me show you

100. shelby1290

okay

101. kohai

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

So lemme fix it ;-;

103. kohai

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104. kohai

I was thinking about it like apples. Lol. You can have 0 apples, but not a negative apple. Anyways

105. kohai

If you have one student, the maximum you'd pay is \$60 for one textbook right?

106. shelby1290

yes that's true so is it correct even if i write down 0?

107. kohai

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

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109. kohai

or

110. kohai

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111. kohai

Does that make sense?

112. shelby1290

Yes, I get it now. Thank you so much!

113. kohai

You're welcome :) I hope I helped. Sorry for the mixup v,v

114. shelby1290

That's totally fine. As long as your explanations make sense! (which they did)

115. shelby1290

thanks again

116. hwyl

set notation is the easiest part of functions http://www.mathsisfun.com/sets/set-builder-notation.html