anonymous
  • anonymous
Medal to whoever gives an acceptable, satisfying answer. When looking at a rational function f(x) = (x - 6)(x + 3)(x + 4) / (x + 6)(x - 3)(x - 4), Jamal and Angie have two different thoughts. Jamal says that the function is defined at x = –6, x = 3, and x = 4. Angie says that the function is undefined at those x values. Who is correct? Justify your reasoning.
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
|dw:1449521343407:dw|
anonymous
  • anonymous
@DariusX Do you think you could help me with this one? I would really appreciate it.
anonymous
  • anonymous
I don't understand.

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More answers

anonymous
  • anonymous
I think the girl might be correct because don't the opposite things cancel each other out?
DariusX
  • DariusX
|dw:1449521674530:dw|
DariusX
  • DariusX
i'm only gonna do the top side, you will do the bottom
DariusX
  • DariusX
|dw:1449521847261:dw|
anonymous
  • anonymous
Okay, so the bottom would be |dw:1449522084926:dw|?
DariusX
  • DariusX
no, not really (x+6)(x-3) = x^2 - 3x + 6x -18 it is also very important to look at the sign before the number in this case you multiply like this: x*x + x*(-3) + 6*x + 6*(-18) = x^2 - 3x + 6x - 18 = x^2 + 3x -18
anonymous
  • anonymous
So, the bottom to your second part is: |dw:1449522644513:dw|
anonymous
  • anonymous
not your second part i mean is this the correction?
DariusX
  • DariusX
yes, now it's correct
anonymous
  • anonymous
Okay nice.
DariusX
  • DariusX
This is answer for the top |dw:1449522899923:dw| now follow these instructions and solve for the bottom
DariusX
  • DariusX
of course it's not final, you have to subtract 4x^2 - 3x^2 = x^2 and -12x-18x = -30x but you probably know that
anonymous
  • anonymous
Okay. Give me one sec.
anonymous
  • anonymous
i'm confused. are the signs going to be minus, plus, minus, again?
DariusX
  • DariusX
no and don't worry there's nothing to be confused about it's very simple if you multiply let's say: -3x(5x - 2) it will be like this: -3x*5x + (-3)*(-2) = -15x + 6 do you understand now? you sum every multiplication, but when multiplying you multiply not only the numbers, but also their signs which are IN FRONT of them.
anonymous
  • anonymous
|dw:1449523630834:dw|
anonymous
  • anonymous
@DariusX
DariusX
  • DariusX
i see it didn't show the full picture. the top was final answer already multiplied with (x+4) and there is also not -18, but -18x
anonymous
  • anonymous
right! i know, sorry. I have been doing math all day and my brain is not functioning as efficiently as i would like.
asnaseer
  • asnaseer
You don't need to expand anything here
asnaseer
  • asnaseer
just look at the terms in the denominator of your rational function
asnaseer
  • asnaseer
you have:\[(x+6)(x-3)(x-4)\]
asnaseer
  • asnaseer
what will the value of this expression be when \(x=-6\)?
anonymous
  • anonymous
I think i just have to justify who is correct for this problem. I don't think i have to do all of this work that I'm drawing out. I just have to explain, like a summary, of why Jamal or Angie is correct. Give me one sec @asnaseer, let me see.
DariusX
  • DariusX
oh yeah, sorry, didn't read the top. when x = –6 or x = 3 or x = 4 the denominator ends up 0 and it can never be 0 if a denominator is 0 then the function is undefined
asnaseer
  • asnaseer
exactly
asnaseer
  • asnaseer
and when the denominator is zero then you are effectively dividing by zero which is undefined
anonymous
  • anonymous
yes. so is Angie correct?
DariusX
  • DariusX
yes, Angie is correct. at those x values function is undefined
asnaseer
  • asnaseer
yup! :)
anonymous
  • anonymous
Great thank you so much! I wish I could give you both a medal. How about you answer my next "hard" question and I'll give one of you a medal for that? I'll post in right now.
asnaseer
  • asnaseer
I am on this site more to help students rather than to collect medals - but thanks any way :)

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