Question

Algebra 2 help please! Will fan and give medal!

When looking at a rational function, Bella and Edward have two different thoughts. Bella says that the function is defined at x = -1, x = 2, and x = 4. Edward says that the function is undefined at those x values. Describe a situation where Bella is correct, and describe a situation where Edward is correct. Is it possible for a situation to exist that they are both correct? Justify your reasoning.

Answer 1

Personally, when I look at a function.. I think "Holy crap, what IS that?!" LOL

Answer 2

Eek! @Mathmale I'm so happy to see you're online so early! Sorry to bother you this early, but, I need some help, please.

Answer 3

Good morning, wherever you are. I'm just out of bed at 5 a.m. in Southern California, and find that my mind is not yet functioning very well.

But anyway. You've already disavowed functions. But let me press the point a little by asking you to tell me what a rational function looks like. Try thinking of examples.

Answer 4

What is your medium of choice when you decide you just have to look something up? A textbook? Encyclopedia Brittanica? The Internet?

Answer 5

Your next-door neighbor?

Answer 6

Please at least glance over the material at this site:

http://en.wikipedia.org/wiki/Rational_function

Answer 7

Holy poop, it's really early for you, then! It's 8:30 am, here in freezing cold Florida.
My medium of choice for looking things up is the internet, but because my mom has Parental Controls on my side of the computer to block every site except for school and OS, that doesn't help any. :(

As for a rational function..
\[\frac{ 2 }{ 5 } + \frac{3}{5x} = \frac{x+5}{10}\]

Answer 8

P.S Bella and Edward -_-

Answer 9

I know Mohammad.. I saw it and was like "Seriously? Wow. -_-"

Answer 10

LOL

Answer 11

I can't escape the sparkly vampires even in school work!

Answer 12

So, if you can't access educational refs on the Internet, then to what resource or resources do you turn when you need info? This is an important question.

Answer 13

books, siblings

Answer 14

I turn to OS, because I don't understand the lessons in the school.

Answer 15

Have you an algebra book handy?

Answer 16

No, I don't have any text books.. At all. .-.

Answer 17

yeah i just have my course books and an engineer father to go along with a two timer math world distinction holder...

Answer 18

You're lucky, Mohammad. xD

Answer 19

yeahhh...

Answer 20

Not to be unkind, but if you're not allowed to look things like this up on the 'Net and you have no ref, then you're walking in the dark.

Is your mom around? If so, do you think she would let you look up that one site I mentioned?

Answer 21

what site

Answer 22

Only thing I really have is a very tired grandpa who's good at math but can't remember how to do most of what I have to do, and OS. So.. Haha..

And she is around, but she's in a VERY bad mood today because we were supposed to go to Disney today, but I didn't get everything I was supposed to yesterday, so we stayed home so I could work. She's throwing a cow, pretty much. .-.

Answer 23

tuition

Answer 24

I'm not a student, Hedgie, although I'm a lifelong learner. I'm a retired Math professor. Having learned so much from books (and more lately from the Internet), I encourage students to look things up when they get stuck through lack of information.

You might want to sit down with your mom when she's feeling better and talk about buying a good Algebra review book and about going onto the 'Net to look up very specific math topics when you need info.

Answer 25

Is your friend Mohammad in the same class? If so, have you shared resources with him and discussed homework questions?

Answer 26

LOL no I live halfway across the world..anyhoo u shud have told us u were a teacher...

Answer 27

I've honestly never talked to Mohammad before now. ^^;;;

But my mom won't remove the blocks so I can look at other helpful sites. She says it's cheating. :(

Answer 28

Mohammad: please define "rational function" for Hedgie's benefit.

Answer 29

Ask your Mom, seriously, how she expects you to obtain info on math topics if you don't have a textbook or reference and are not allowed to look up technical subjects on the 'Net.

Answer 30

Mohammad?

Answer 31

yess..

Answer 32

Can you help with a definition of "rational function"?

Answer 33

Well, I have the online lessons. I've asked before, and she's said "Go reread the lessons as many times as you need to, before you understand what to do."

Answer 34

Where "halfway around the world" are you located, and do you have math textbooks on hand?

Answer 35

Have you looked up "rational function" in that lesson material?

Answer 36

a rational function is one on which power of numerator<power of denominator

Answer 37

I would, MM, but I'm in the middle of a test, and if I go look back, it'll close out the test and I'll lose all my answers.

Answer 38

Glad to have the beginnings of a definition. Actually, Mohammed, you've helped by pointing out that a rational function has a numerator and a denominator.
What else could you tell Hedgie about rational functions? Could you give her / him (????) an example?

Answer 39

I'm a girl, MM. LOL

Answer 40

Hedgie: Is yours a multiple choice test, or "fill in the blanks"?

Answer 41

It's a Fill in the blanks. .-.

Answer 42

hedgie we're right here if u need any help..

Answer 43

I've asked for help, but this question isn't being answered at the moment. xD
Oh well, I know ya'll are trying to help. :)

Answer 44

y=x/(x^2+1) is an example

Answer 45

And if you're trying to tell me what a rational expression is because of my comment about how I think "Holy crap, what the heck is that?!" about them, I was trying to be funny with it. I wasn't serious. LOL

Answer 46

no MM asked me for an example to give to u

Answer 47

That was to MM, Mohammad.. ^^;;;

Answer 48

(Experiencing Internet connection problems.)

I've looked up "rational function" on the 'Net. (My mother is 97 years old so has not set up any parental controls). With thanks to wikipedia:

In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers.

Answer 49

I'm going to set up a rational function of my own and ask you and Mohammad to discuss it and determine where it is defined and where it is not.

Answer 50

\[f(x)=\frac{ x-5 }{ (x+1)(x-3)(x-1)^{2}}\]

Answer 51

Where (for which x) is this function defined?
Where (for which x) is this function not defined?

Answer 52

Why?

Answer 53

BRB (be right back). But you two have plenty to discuss regarding this math topic.

Answer 54

not defined -1,3,1
defined for all other values of x

Answer 55

Would you feel confident explaining your reasoning to Hedgie?

Answer 56

wud u brb

Answer 57

I am here, but am going to read the paper while y ou and Hedgie discuss this. Just type something in when you want me back.

Answer 58

Hedgie, what's your point of view on the question I've asked you and M?
Could you, on your own, set up a rational function that is not defined at x=2 or x=-3?

Answer 59

Hedgie? Hope you're not AWOL. :)

Answer 60

Sorry for poofing, I had to go do something!

Answer 61

As I told you when excusing myself, I'd like for you to do the same. We've had some good discussions, and iappreciate that, but yesterday there were some long gaps between some of your responses to my questions.

Answer 62

Please, go back and look at the 2 questions I've asked you.

Answer 63

????anybody need me here

Answer 64

I'm sorry about that. ^^;;;
And yesterday wasn't me going places or whatever, it was OS lagging. ^^;;;;

Answer 65

OK. Please respond as best you can to the two questions I've asked you:

Hedgie, what's your point of view on the question I've asked you and M?
Could you, on your own, set up a rational function that is not defined at x=2 or x=-3?

Answer 66

For planning purposes, is Mohammad still with us or not?

Answer 67

yeah

Answer 68

mathmale are you hedgie's teacher or something

Answer 69

M: I'm glad you're involved. Feel free to help Hedgie all you can with suggestions.

Answer 70

I think defined is -1, 3, 1..
And the rest are undefined.

And as for creating my own expression.. I have no idea. .-. The whole reason I'm asking for help on this one is because I have no idea how to create what they want.

Answer 71

No, I'm simply an Open Study participant, as is Hedgie. I happen to be a retired professor.

Answer 72

Both Moh. and I have created rational expressions: go back and take a look.

One of the simplest would be f(x)=x/(x-2).

Answer 73

\[f(x)=\frac{ x }{ x-2 }\]

Answer 74

Where (for which x values) would that be defined?

Answer 75

In that one, the -2 would be defined, right?

Answer 76

Moh: step in any time you want to comment. My goal is to encourage you two to work together.

Answer 77

Moh: pls responde to Hedgie's question.

Answer 78

oh sorrryy got into another question...
hadgie u need to understand that a fractioon is defined when the denominator(lower one) is not zero it can be lower it can be higher but not zero..

Answer 79

so for the fraction x/(x-2) to be defined x needs to be anything but 2 as 2-2 is zero

Answer 80

Right. Okay?

Answer 81

So, Moh is saying that the rational function I gave you is defined so long as the denominator (use that technical term, please) is not zero.

Hedgie, please take that denominator, set it = to zero, and solve for x.
Whatcha get?

Answer 82

Moh: involve yourself as much as y ou want (preferably more than less).

Answer 83

ok

Answer 84

thanks... you really are contributing here, and I appreciate it

Answer 85

No problem...

Answer 86

I get 2.

Answer 87

Hedgie? Feel free to ask Moh questions if you like.

Answer 88

Good. Now please explain the significance of that 2.

Answer 89

The 2 will set the denominator to zero if it's plugged into x.

Answer 90

great so the fraction will be defined(meaning the denominator will not be zero) when the value of x is not 2

Answer 91

That's right. So, write a sentence regarding where this rational function is and is not defined. Moh has already partially addressed this.

Answer 92

So the numbers in the denominator are NOT the defined ones?

Answer 93

Moh?

Answer 94

please call me ARQUM...Mohammad is a sacred name of my religion

Answer 95

Hedgie: We're discussing where the FUNCTION is defined or undefined, so it's up to you to explain for which values of x this or that is true. Arqum: absolutely! Forgive me for not knowing that.

Answer 96

hmm so hedgie do u understand...
no problem MM

Answer 97

Hedgie: Please look at what Arqum typed a few min. ago. He was on the right track.

Answer 98

When looking at a rational function, Bella and Edward have two different thoughts. Bella says that the function is defined at x = -1, x = 2, and x = 4.

Could you two work together to create a new rational function that is NOT defined at x = -1, x = 2, and x = 4 ? (We are now working on theproblem that Hedgie has posted.)