Results 1 to 3 of 3
Like Tree2Thanks
  • 1 Post By skeeter
  • 1 Post By romsek

Thread: Find the domain of each rational function. Do not graph the function.

  1. #1
    Senior Member
    Joined
    Jul 2015
    From
    United States
    Posts
    372
    Thanks
    6

    Find the domain of each rational function. Do not graph the function.

    Hi, I need help on two problems.

    23. f(x)=2x^2+7x-2/x^2-25 --> the answer for that one is : (- negative infinity, -5)U(5,5)U(5, positive infinity) My question is why is the answer (5,5) included in there.

    25. f(x)= x-1/x^3-x --> the answer is (negative infinity,-1)U(-1,0)U(0,1)U(1,positive infinity) I had no idea how to do this problem.


    All help is appreciated.

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,047
    Thanks
    3621

    Re: Find the domain of each rational function. Do not graph the function.

    Quote Originally Posted by math951 View Post
    Hi, I need help on two problems.

    23. f(x)=(2x^2+7x-2)/(x^2-25) --> the answer for that one is : (- negative infinity, -5)U(5,5)U(5, positive infinity) My question is why is the answer (5,5) included in there.

    25. f(x)= (x-1)/(x^3-x) --> the answer is (negative infinity,-1)U(-1,0)U(0,1)U(1,positive infinity)
    in future, please use parentheses as grouping symbols

    #22 it should be $(-5,5)$, not $(5,5)$

    $\dfrac{2x^2+7x-2}{x^2-25} = \dfrac{2x^2+7x-2}{(x-5)(x+5)}$

    the denominator, $x^2-25 = 0$ at $x = \pm 5$. the vertical asymptotes at these two x-values break up the real number line into three regions ...

    $(-\infty,5) \cup (-5,5) \cup (5,\infty)$

    #25 $\dfrac{x-1}{x^3-x} = \dfrac{x-1}{x(x^2-1)} = \dfrac{x-1}{x(x-1)(x+1)}$

    vertical asymptotes at $x=0$ and $x=-1$ ... a point discontinuity (a "hole") at $x=1$

    domain is $(-\infty,-1) \cup (-1,0) \cup (0,1) \cup (1, \infty)$
    Thanks from math951
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,609
    Thanks
    2369

    Re: Find the domain of each rational function. Do not graph the function.

    Quote Originally Posted by math951 View Post
    Hi, I need help on two problems.

    23. f(x)=2x^2+7x-2/x^2-25 --> the answer for that one is : (- negative infinity, -5)U(5,5)U(5, positive infinity) My question is why is the answer (5,5) included in there.

    25. f(x)= x-1/x^3-x --> the answer is (negative infinity,-1)U(-1,0)U(0,1)U(1,positive infinity) I had no idea how to do this problem.


    All help is appreciated.

    Thank you.
    23) the answer is wrong. The correct answer is $(-\infty, -5) \cup (-5, 5) \cup (5, \infty)$

    Someone left out a negative sign.

    25) $f(x) = \dfrac{x-1}{x^3-x} = \dfrac{x-1}{x(x^2-1)}$

    the points where this is undefined are $x=0, -1, 1$ and thus the domain is

    $(-\infty, -1)\cup (-1 ,0) \cup (0,1) \cup (1, \infty)$
    Last edited by romsek; Nov 15th 2015 at 09:10 AM.
    Thanks from math951
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Domain of a rational function
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Aug 27th 2011, 07:42 PM
  2. Rational Function Graph
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Jan 1st 2010, 04:04 PM
  3. graph of a rational function
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Sep 8th 2009, 09:06 PM
  4. Replies: 1
    Last Post: Oct 19th 2008, 11:31 AM
  5. Determine the domain of a rational function
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: Jun 30th 2008, 04:56 PM

Search Tags


/mathhelpforum @mathhelpforum