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Math Help - Rational Function

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    Rational Function

    g(x)=2 - 3x^2/X^2 - 1 => 2 - 3x^2 divided by x^2 - 1

    How to find asymptotes and intercepts?
    Thx
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Snowboarder View Post
    g(x)=2 - 3x^2/X^2 - 1 => 2 - 3x^2 divided by x^2 - 1

    How to find asymptotes and intercepts?
    Thx
    if you are asking what the intercepts and asymptotes of f(x)=\frac{2-3x^2}{x^2-1} are you do this

    y-asymp take the \lim_{x \to {\pm\infty}}\frac{2-3x^2}{x^2-1}

    x-asymp..find the values that make the top 0 but not the bottom 0

    x-int...set it equal to 0 and solve...remember in a rational function the only part that makes the function 0 is the numerator...so just solve the numerator of 0

    y-int...just take f(0)
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Snowboarder View Post
    g(x)=2 - 3x^2/X^2 - 1 => 2 - 3x^2 divided by x^2 - 1

    How to find asymptotes and intercepts?
    Thx
    O and also this is more of a Pre-calc question..this forum is generally for abstract algebra and the like...but its fine! haha just next time put it in Urgent if you dont know where else to go...it will be answered more quickly also
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by Snowboarder View Post
    g(x)=2 - 3x^2/X^2 - 1 => 2 - 3x^2 divided by x^2 - 1

    How to find asymptotes and intercepts?
    Thx

    Find the the asymptotes of

    g(x)=\frac{2-3x^2}{x^2-1} I think this is what you mean

    Please use parenthsis to make it clear

    Our rule for horizontal asympototes is:

    if the degree of the numerator is bigger than the degree on the denomitor there isn't one

    if the degree of the numerator and denominator are equal it is the ratio of the lead coeffeints

    if the degree of the denominator is bigger than the numerator it is the line y=0.

    we need the 2nd rule so the asymptote is y=\frac{-3}{1}=-3

    to find vertical asymptotes we set the denominator equal to zero.

    x^2-1=0 \iff (x-1)(x+1)=0,x= \pm 1

    so x=1 and x=-1 are the vertical asymptotes

    to find the intercepts you set the opposite variable = to zero

    x-int set y=0

    0=\frac{2-3x^2}{x^2-1} \iff 0=2-3x^2 \iff 3x^2=2 \iff x =\pm \sqrt{\frac{2}{3}}


    y-int set x=0
    y=\frac{2-3(0)^2}{0^2-1}=-2

    Rational Function-.jpg

    I hope this helps
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