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Math Help - Finding holes in a function! Help please!

  1. #1
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    Exclamation Finding holes in a function! Help please!

    Can you please find the hole(s) in these three functions?

    f(x) = x^2-x-6 / 2x^2 -x- 6


    f(x) = -x^3-7x^2-12x / 3x^2-11x-20


    f(x) = x^2+4x-5 / x^4-4x^3+3x^2


    Thanks so much! If you can't do one don't worry about it! All the work helps!
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  2. #2
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    Hello, Sbach2010!

    Find the hole(s) in these three functions.

    . . f(x) \:= \:\frac{x^2-x-6}{2x^2 -x- 6}

    Factor: . f(x) \;=\;\frac{(x+2)(x-3)}{(x-2)(2x+3)}

    It has vertical asymptotes at: . x \,=\,2\text{ and }x \,=\,-\tfrac{3}{2}
    . . but no holes



    f(x) \:= \:\frac{-x^3-7x^2-12x}{3x^2-11x-20}

    Factor: . f(x)\;=\;\frac{-x(x+3)(x+4)}{(x-5)(3x+4)}

    It has vertical asymptotes at: . x\,=\,5\text{ and }x\,=\,-\tfrac{4}{3}
    . . but no holes.



    f(x) \:= \:\frac{x^2+4x-5}{x^4-4x^3+3x^2}

    Factor: . f(x)\;=\;\frac{(x-1)(x+5)}{x^2(x-1)(x-3)}

    It has vertical asymptotes at: . x \,=\,0\text{ and }x\,=\,3

    . . and a hole at (1, -3).

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  3. #3
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    Thank you that was very helpful!

    Now what are the x and y intercepts for each funtion?

    Also the Domain of each?

    Help much appreciated!
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  4. #4
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    To find the y-intecept, you need to set x = 0 for the equation
    To find the x-intecept, you need to set y = 0 for the equation
    To find the domain of the function, you can refer to this useful link for guidance 2a. Domain and Range of a Function

    Hope it helps.

    Quote Originally Posted by Sbach2010 View Post
    Thank you that was very helpful!

    Now what are the x and y intercepts for each funtion?

    Also the Domain of each?

    Help much appreciated!
    Follow Math Help Forum on Facebook and Google+

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