Question

When looking at a rational function, Jamal and Angie have two different thoughts. Jamal says that the function is defined at x = −3, x = −4, and x = 6. Angie says that the function is undefined at those x values. Describe a situation where Jamal is correct, and describe a situation where Angie is correct. Is it possible for a situation to exist where they are both correct?

Answer 1

For Jamal could I say he is correct if the function is (x + 3)(x + 4)(x - 6)/6

Answer 2

@Directrix could you help me again?

Answer 3

From the wording in the question, do you think Jamal and Angie are both looking at the same function?

Answer 4

Maybe. But it says describe a situation where they'd both be correct.

Answer 5

I came up with this:
Jamal would be correct if the function were (x + 3)(x + 4)(x - 6)/6 or (-3 + 3)(x + 4)(x - 6). He would be correct because the solution would be 0/6 or 0.

Angie would be correct if the function were 3/(x + 3)(x + 4)(x - 6) or 3/(-3 + 3)(-4 + 4)(6 - 6). The function would be undefined at those x values because the denominator would equal 0.

Answer 6

Because if it is the same function, both J and A could not both be correct because a given function is or is not defined at specific points.

Answer 7

I think I'm supposed to just come up with a function where they'd both be correct, like I did

Answer 8

y =[ (x + 3)(x + 4)(x - 6)] /6

This function is defined at x = -3, x = -4 and x = 6.

How could Angie say the same function is not defined at these points?

Answer 9

She could say it's not defined because the solution is 0?

Answer 10

Angie could look at the reciprocal of that function and then her statements would be true.

y = 6 / [ (x + 3)(x + 4)(x - 6)]

Answer 11

0 and undefined are not the same concept.

Answer 12

So I should just use the same function but flipped for Angie?

Answer 13

5/0 is undefined but 0/5 = 0 and is, of course, defined.

Answer 14

Let me think. When the function is flipped, it becomes a different function.

Answer 15

I think that would make sense though. It would become a different function but I think that's fine for this question

Answer 16

Because at the end it asks for a situation where they are both correct

Answer 17

This is what I have now -

Jamal would be correct if the function were (x + 3)(x + 4)(x - 6)/6 or (-3 + 3)(-4 + 4)(6 - 6)/6. He would be correct because the solution would be 0/6 or 0 which is defined.

Angie would be correct if she looked at the reciprocal of Jamal's function which is 6/(x + 3)(x + 4)(x - 6) or 6/(-3 + 3)(-4 + 4)(6 - 6). The function would be undefined at those x values because the denominator would equal 0.

Answer 18

Look at this attachment. Let's talk about it.

Answer 19

I saw that and thought it was a good example...I was trying to change mine up to avoid plagiarism

Answer 20

I don't know why people do not write y= when writing a function.
Anyway, look at the function that is said to be the one where J and K are both correct.

Answer 21

I am not advocating plagiarism. I'm looking at how other people have interpreted this problem.

Answer 22

That attachment comes from here:
http://openstudy.com/updates/52ad5647e4b0b09acc7f8ce5

Answer 23

The function would be y = 0/0. Wouldn't this be undefined because of the denominator being 0?

Answer 24

Angie correct, Jamal wrong:

y =[ (x + 3)(x + 4)(x - 6)] /6 This function is defined at x = -3, x = -4 and x = 6.

Answer 25

And wouldn't Angie be incorrect there since that would be y = 0/6 which is defined?

Answer 26

This is thought of as indeterminate. 0/0

Division is defined in terms of multiplication.
6 divided by 2 = 3 if and only if 2*3 =6

5/0 is undefined because there is no number times 0 which gives 5.

Answer 27

On 0/0, any number times 0 = 0 so you could say that every number in the world could = 0/0. So, it is indeterminate. Most people just say division by 0 is undefined.

Answer 28

Ah ok, so saying they are both correct if the function is y=(x + 3)(x + 4)(x - 6)/(x + 3)(x + 4)(x - 6) would be correct?

Answer 29

Or not really because it's neither defined or undefined

Answer 30

Before we get to both correct, if that is true.

On what equation was Jamal correct and Angie wrong?

Answer 31

Jamal was correct on y=(x + 3)(x + 4)(x - 6)/6

Answer 32

And Angie was wrong on that one because the function is defined

Answer 33

This function where both are supposedly correct seems off to me.

Answer 34

I don't think it's possible for them to both be right on that function because it's not defined or undefined

Answer 35

Was my other answer correct?

Answer 36

Many people would take y = y=[(x + 3)(x + 4)(x - 6])/[(x + 3)(x + 4)(x - 6)] and say that it is really just y = 1 after the common factors are divided out.

Answer 37

That's true

Answer 38

But, that is not true because to divide, say (x+3) by (x + 3), you would have to say that the answer is y = 1 where x is not equal to -3. So, the answer is y = 1 with a hole at the point (-3, 1).

Answer 39

Y = (x^2 - 1)/(x - 1) does not have the same graph as y = x + 1. They are close but not the same.

Answer 40

I'm thinking there isn't a situation where they could both be correct

Answer 41

We divide that stuff out all the time in Algebra without specifying that certain values of x have to be excluded.

Answer 42

I agree with you.

I do think that there is a function where the two of them THINK they are both right. But, thinking they are right does not make their thinking correct.

Answer 43

Let's look at the problem again.

Answer 44

I just don't see how a function could be defined and undefined at the same x values

Answer 45

>> Is it possible for a situation to exist where they are both correct?
No, there cannot be.

Answer 46

Sounds good

Answer 47

>>I just don't see how a function could be defined and undefined at the same x values

Right. That is against the consistency of mathematics.

Answer 48

Whoever wrote that question is not a math person. Math people write cleanly and crisply and leave nothing to chance interpretation. So, if the computer or whatever says "wrong" on this, then we must protest.

Answer 49

Well after my teacher grades it I will try to let you know what he says

Answer 50

Can I show you my entire answer and we can rreview it?

Answer 51

Yes, and speak up for the mathematics we discussed and don't back down.

Answer 52

Yes, do that.

Answer 53

Jamal would be correct if the function were f(x)=(x + 3)(x + 4)(x - 6)/6. He would be correct because the solution would be 0/6 or 0 which is defined.

Angie would be correct if she looked at the reciprocal of Jamal's function which is f(x)=6/(x + 3)(x + 4)(x - 6). The function would be undefined at those x values because the denominator would equal 0.

It is not possible for a situation to exist where they are both correct because a function can't be defined and undefined at the same x values.

Answer 54

>> He would be correct because the solution would be 0/6 or 0 which is defined.

I get what you are saying but 0 is not a solution to that function.

Jamal would be correct if the function were f(x)=(x + 3)(x + 4)(x - 6)/6. He would be correct because the function is defined at the points where x = - 3, -4, and 6. The value of the function at any one of those x-values would be 0.

Answer 55

So just change my wording?

Answer 56

Angie would be correct if she looked at the reciprocal of Jamal's function which is f(x)=6/[(x + 3)(x + 4)(x - 6)]. The function would be undefined at those x values of -4, -4, and 6 because any one of those 3 x-values would cause the denominator to equal 0.

Answer 57

ok I got it :)

Answer 58

A function is undefined at a point but a function is not just globally undefined.

It is a concept of undefined at a point.

Answer 59

And, a big no on that third part. As you said, how can the function be simultaneously defined and undefined at the same points.

Answer 60

Exactly. I think we've got this one figured out

Answer 61

Alrighty, then. I so enjoyed the discussion with full participation on the part of us both. Let's do it again sometime, okay?

Answer 62

Okay :) Thank you again for all of your help!