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).

- shelby1290

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- 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

OKAY LET US TRY

- hwyl

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

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- shelby1290

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

- hwyl

THIS IS JUST A HYPOTHETICAL QUESTION

- hwyl

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

- shelby1290

$60.00

- hwyl

GOOD SO LET US CREATE A TABLE

- hwyl

|dw:1442095256587:dw|

- hwyl

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

- hwyl

buy the book for each of you to own

- hwyl

make sense

- hwyl

let us update our table

- shelby1290

$120.00

- hwyl

|dw:1442095394341:dw|

- hwyl

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

- shelby1290

$1,200

- hwyl

cool!
so how about you update our table

- shelby1290

what do i plug in for the x-values?

- hwyl

|dw:1442095582413:dw|

- 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

DO YOU NOW FIGURE OUT HOW TO CREATE FUNCTIONS?

- shelby1290

|dw:1442095906271:dw|

- shelby1290

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

- shelby1290

And can you please stop typing in all capital letters?

- 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

i like CAPS

- shelby1290

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

- shelby1290

@hwyl ^

- hwyl

I put it in box lol

- shelby1290

But how do I create an EQUATION ?

- kohai

Okay, so you were on the right track

- 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

Do you understand why that is the equation?

- shelby1290

yes because 60 is the cost for the textbook

- 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

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

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

- kohai

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

- shelby1290

linear because it has a degree of 1?

- kohai

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

- kohai

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

- shelby1290

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

- kohai

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

- kohai

Now, what do you know about domain and range

- shelby1290

Domain is {XER} and range is {YER}

- shelby1290

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

- 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

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

- shelby1290

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

- 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

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

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

- kohai

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

- shelby1290

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

- shelby1290

|dw:1442098912668:dw|

- shelby1290

I'm not sure

- 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

You know what I mean?

- shelby1290

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

- 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

So the notation that's generally used for that is

- kohai

\[x \le 30\]

- kohai

That says that x is less than or equal to 30

- shelby1290

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

- 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

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

- kohai

Can you show me an example?

- shelby1290

i think im getting the differences mixed up

- kohai

Oh, I see, okay. So when you have like,
0

- kohai

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

- kohai

|dw:1442099479057:dw|

- kohai

Glad you pointed that out :)

- shelby1290

|dw:1442099423813:dw|

- shelby1290

Like that or something ^

- shelby1290

yes

- kohai

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

- shelby1290

like the way domains are set up?

- kohai

Yeah, that

- kohai

And why you should do 0

- shelby1290

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

- 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

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

- shelby1290

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

- shelby1290

{YER|0

- kohai

Kind of. You have the right idea

- kohai

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

- kohai

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

- kohai

(Not a trick question)

- shelby1290

0

- kohai

Yes, good

- kohai

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

- shelby1290

30

- 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

$1,800

- kohai

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

- shelby1290

{YER| 30>y>1800}

- kohai

Close

- kohai

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

- shelby1290

okay

- 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

So lemme fix it ;-;

- kohai

|dw:1442100303626:dw|

- kohai

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

- kohai

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

- shelby1290

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

- 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

|dw:1442100443760:dw|

- kohai

or

- kohai

|dw:1442100503454:dw|

- kohai

Does that make sense?

- shelby1290

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

- kohai

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

- shelby1290

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

- shelby1290

thanks again

- hwyl

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

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