anonymous
  • anonymous
Im confused can someone help me?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@Michele_Laino i dont understand how to solve these?
1 Attachment
Michele_Laino
  • Michele_Laino
question #1 for example if I have this rational function: \[f\left( x \right) = \frac{1}{{{x^2} + 2x}}\] then, in order to find the asymptotes, I try to factorize the quantity: \(x^2+2x\)
anonymous
  • anonymous
0?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Michele_Laino
  • Michele_Laino
hint: I try to factorize the denominator, since \(x^2+2x\) is the denominator of my function above. So what is the right option?
anonymous
  • anonymous
So C
Michele_Laino
  • Michele_Laino
please wait a moment, what is the maning of "holes" of a function?
anonymous
  • anonymous
well its asking if theres any holes in the graph I'm not sure what it means
Michele_Laino
  • Michele_Laino
yes! oops.. meaning*
anonymous
  • anonymous
How do we figure out number 2?
Michele_Laino
  • Michele_Laino
I understand, the hole of a graph is a point x such that the function assumes an infinite value so the answer to first question is option C, then you are right!
Michele_Laino
  • Michele_Laino
I'm sorry, the right answer to question #1 is option D
Michele_Laino
  • Michele_Laino
we have to factorize both numerator and denominator
anonymous
  • anonymous
okay what about the 2nd one?
Michele_Laino
  • Michele_Laino
question #2 here we can factorize both numerator an denominator as follows: \[f\left( x \right) = - \frac{{\left( {x - 1} \right)\left( {x + 3} \right)}}{{\left( {x - 1} \right)\left( {x + 2} \right)}}\]
anonymous
  • anonymous
i dont get what the answer choice would be?
Michele_Laino
  • Michele_Laino
as I wrote before, in order to understand if the function has some holes, we have to factorize both numerator and denominator. Now, in my factorization above, you can cancel two factors, do you know what are such factor?
anonymous
  • anonymous
C?
anonymous
  • anonymous
or D could be the answers
Michele_Laino
  • Michele_Laino
hint: after a simplification, I can write this: \[f\left( x \right) = - \frac{{\left( {x - 1} \right)\left( {x + 3} \right)}}{{\left( {x - 1} \right)\left( {x + 2} \right)}} = - \frac{{x + 3}}{{x + 2}}\] as we can see at \(x=2\) our function is continuous, so, it can not be option C, and for the same reason it can not be option D
anonymous
  • anonymous
B
Michele_Laino
  • Michele_Laino
that's right!
anonymous
  • anonymous
(: what about the 3rd one?
Michele_Laino
  • Michele_Laino
question #3 hint: such function is a rational function, and it is given by the quotient between these two polynomials: \(x+2\) and \(x-2\)
anonymous
  • anonymous
A
Michele_Laino
  • Michele_Laino
that's right!
anonymous
  • anonymous
Can you help me with 2 more ?
1 Attachment
Michele_Laino
  • Michele_Laino
question #4 as I wrote before, I can rewrite the function like below: \[f\left( x \right) = - \frac{{\left( {x - 1} \right)\left( {x + 3} \right)}}{{\left( {x - 1} \right)\left( {x + 2} \right)}} = - \frac{{x + 3}}{{x + 2}}\] now, please what are the values \(x\) such that the denominator is equal to zero?
anonymous
  • anonymous
2?
Michele_Laino
  • Michele_Laino
we have to solve this equation: \(x+2=0\), so what is \(x\) ?
anonymous
  • anonymous
-2
Michele_Laino
  • Michele_Laino
that's right, so how many asymptotes we have?
anonymous
  • anonymous
0?
Michele_Laino
  • Michele_Laino
please we have the only asymptote \(x=-2\), am I right?
anonymous
  • anonymous
D?
Michele_Laino
  • Michele_Laino
\(x=-2\) is a vertical asymptote
anonymous
  • anonymous
oh so B then?
Michele_Laino
  • Michele_Laino
that's right!
anonymous
  • anonymous
and #5?
Michele_Laino
  • Michele_Laino
question #5 I have already answered to that question, when I wrote this formula: \[\begin{gathered} f\left( x \right) = \frac{{3 - 2x - {x^2}}}{{{x^2} + x - 2}} = \hfill \\ \hfill \\ = - \frac{{\left( {x - 1} \right)\left( {x + 3} \right)}}{{\left( {x - 1} \right)\left( {x + 2} \right)}} = - \frac{{x + 3}}{{x + 2}} \hfill \\ \end{gathered} \]
anonymous
  • anonymous
B
Michele_Laino
  • Michele_Laino
that's right! please, when you have to do similar exercises, remember to factorize both numerator and denominator of the rational function
anonymous
  • anonymous
Okay thank you so much! (:
Michele_Laino
  • Michele_Laino
:)

Looking for something else?

Not the answer you are looking for? Search for more explanations.