shelby1290
  • shelby1290
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).
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
shelby1290
  • 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.
hwyl
  • hwyl
OKAY LET US TRY
hwyl
  • hwyl
IF YOU WANT TO BUY THIS BOOK, HOW MUCH WOULD YOU PAY?

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shelby1290
  • shelby1290
@hwyl i wouldn't even buy it, i don't like math lol
hwyl
  • hwyl
THIS IS JUST A HYPOTHETICAL QUESTION
hwyl
  • hwyl
IF YOU WERE TO BUY A $60.00 BOOK, HOW MUCH WOULD YOU EXPECT TO PAY?
shelby1290
  • shelby1290
$60.00
hwyl
  • hwyl
GOOD SO LET US CREATE A TABLE
hwyl
  • hwyl
|dw:1442095256587:dw|
hwyl
  • hwyl
let us say you and your friend wanted to buy the book, how much you two pay?
hwyl
  • hwyl
buy the book for each of you to own
hwyl
  • hwyl
make sense
hwyl
  • hwyl
let us update our table
shelby1290
  • shelby1290
$120.00
hwyl
  • hwyl
|dw:1442095394341:dw|
hwyl
  • hwyl
let us say that 20 students needed to buy the book, how much would it sum to?
shelby1290
  • shelby1290
$1,200
hwyl
  • hwyl
cool! so how about you update our table
shelby1290
  • shelby1290
what do i plug in for the x-values?
hwyl
  • hwyl
|dw:1442095582413:dw|
hwyl
  • 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
hwyl
  • hwyl
DO YOU NOW FIGURE OUT HOW TO CREATE FUNCTIONS?
shelby1290
  • shelby1290
|dw:1442095906271:dw|
shelby1290
  • shelby1290
What do you mean by " do i now know how to create functions?"
shelby1290
  • shelby1290
And can you please stop typing in all capital letters?
hwyl
  • 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
hwyl
  • hwyl
i like CAPS
shelby1290
  • shelby1290
Oh okay then no i don't know how to write an equation in function notation for part a)
shelby1290
  • shelby1290
@hwyl ^
hwyl
  • hwyl
I put it in box lol
shelby1290
  • shelby1290
But how do I create an EQUATION ?
kohai
  • kohai
Okay, so you were on the right track
kohai
  • 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)
kohai
  • kohai
Do you understand why that is the equation?
shelby1290
  • shelby1290
yes because 60 is the cost for the textbook
kohai
  • 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
kohai
  • 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
kohai
  • kohai
So you've already done part A. f(x) = 60x
kohai
  • kohai
Do you know what kind of graph this would be? Linear vs quadratic?
shelby1290
  • shelby1290
linear because it has a degree of 1?
kohai
  • kohai
Very good, very good. You just did part b :) So it would be a straight line
kohai
  • kohai
So if you wanted to see how much it would cost to buy 30 books, do you know what you would do?
shelby1290
  • shelby1290
f(30)=60(30) = $1,800
kohai
  • kohai
You even have proper notation, nice. See, you're doing just fine :)
kohai
  • kohai
Now, what do you know about domain and range
shelby1290
  • shelby1290
Domain is {XER} and range is {YER}
shelby1290
  • shelby1290
I don't really understand how to set them up when i have a bunch of numbers.
kohai
  • 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?
shelby1290
  • shelby1290
I know that i'll need greater and less than signs but idk where to place them
shelby1290
  • shelby1290
nooo don't say that lol i'm terrible at math. that's why im here asking a billion questions
kohai
  • 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
kohai
  • 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.
kohai
  • kohai
So that means there will be an "-or equal to" in there
kohai
  • kohai
So think about it, will it be "greater than or equal to" 30 students, or "less than or equal to" 30 students?
shelby1290
  • shelby1290
I'm one of them haha and what you said is true. I do need extra help.
shelby1290
  • shelby1290
|dw:1442098912668:dw|
shelby1290
  • shelby1290
I'm not sure
kohai
  • 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?
kohai
  • kohai
You know what I mean?
shelby1290
  • shelby1290
so all i'm changing is the greater than signs to less thans ?
kohai
  • 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
kohai
  • kohai
So the notation that's generally used for that is
kohai
  • kohai
\[x \le 30\]
kohai
  • kohai
That says that x is less than or equal to 30
shelby1290
  • shelby1290
ah okay so..|dw:1442099289067:dw|
kohai
  • 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
shelby1290
  • shelby1290
what does it mean when you have two numbers inside of the brackets like i did before?
kohai
  • kohai
Can you show me an example?
shelby1290
  • shelby1290
i think im getting the differences mixed up
kohai
  • kohai
Oh, I see, okay. So when you have like, 0
kohai
  • kohai
So for the purposes of this example, yeah, add that in
kohai
  • kohai
|dw:1442099479057:dw|
kohai
  • kohai
Glad you pointed that out :)
shelby1290
  • shelby1290
|dw:1442099423813:dw|
shelby1290
  • shelby1290
Like that or something ^
shelby1290
  • shelby1290
yes
kohai
  • kohai
So you understand what that means now yeah? And why it should be included?
shelby1290
  • shelby1290
like the way domains are set up?
kohai
  • kohai
Yeah, that
kohai
  • kohai
And why you should do 0
shelby1290
  • shelby1290
Because you haven't bought the textbook yet so you start with 0? I don't know
kohai
  • 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
kohai
  • kohai
If we had just x<30, it would mean any number less than 30. That means you could have like -600 students, theoretically
shelby1290
  • shelby1290
ahh okay i see. does the same thing go for the range?
shelby1290
  • shelby1290
{YER|0
kohai
  • kohai
Kind of. You have the right idea
kohai
  • kohai
So in the range's case, it's all the y-values. So the y-values is the amount paid for textbooks
kohai
  • kohai
So what's the lowest value you can pay for a textbook?
kohai
  • kohai
(Not a trick question)
shelby1290
  • shelby1290
0
kohai
  • kohai
Yes, good
kohai
  • kohai
So, what is the highest amount you will pay if you have a maximum of 30 students?
shelby1290
  • shelby1290
30
kohai
  • 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
shelby1290
  • shelby1290
$1,800
kohai
  • kohai
Yup! So what's the range going to be?
shelby1290
  • shelby1290
{YER| 30>y>1800}
kohai
  • kohai
Close
kohai
  • kohai
30 has exclusively to do with x, so it's not going to be in there. Let me show you
shelby1290
  • shelby1290
okay
kohai
  • 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
kohai
  • kohai
So lemme fix it ;-;
kohai
  • kohai
|dw:1442100303626:dw|
kohai
  • kohai
I was thinking about it like apples. Lol. You can have 0 apples, but not a negative apple. Anyways
kohai
  • kohai
If you have one student, the maximum you'd pay is $60 for one textbook right?
shelby1290
  • shelby1290
yes that's true so is it correct even if i write down 0?
kohai
  • 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
kohai
  • kohai
|dw:1442100443760:dw|
kohai
  • kohai
or
kohai
  • kohai
|dw:1442100503454:dw|
kohai
  • kohai
Does that make sense?
shelby1290
  • shelby1290
Yes, I get it now. Thank you so much!
kohai
  • kohai
You're welcome :) I hope I helped. Sorry for the mixup v,v
shelby1290
  • shelby1290
That's totally fine. As long as your explanations make sense! (which they did)
shelby1290
  • shelby1290
thanks again
hwyl
  • hwyl
set notation is the easiest part of functions http://www.mathsisfun.com/sets/set-builder-notation.html

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