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Thread: Find the domain, zeroes and asymptotes of an absolute value function

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    Find the domain, zeroes and asymptotes of an absolute value function

    Hey guys, I am having a little bit of trouble with this question and I would really appreciate any help you can give me. If you can give me a step by step answer to this question, it would be greatly appreciated!!
    The equation is f(x) = |x^2-9|^-3/4
    They want me to find the domain, zeroes, and vertical/ horizontal asymptotes and then graph the function.
    Thanks in advance!
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    Re: Find the domain, zeroes and asymptotes of an absolute value function

    Already completed one problem for you in this forum.

    Now it's your turn ... show what you have completed for this one.
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    Re: Find the domain, zeroes and asymptotes of an absolute value function

    Hey, I actually finished the problem but I am not sure it's right. I think the horizontal asymptote is at y=0, the vertical asymptotes are at x=3, and x=-3 and xER but x DNE at x=3, -3. I just wanted to check my work with someone because when I tried to find the answer on the calculator, my calculations were different than what the calculator said and I wanted to make sure I had the right answer. I drew out the graph which you will see in the attached image. I will take a picture of what I did and then if someone can just double check to make sure I have it right?Find the domain, zeroes and asymptotes of an absolute value function-img_0256.jpgFind the domain, zeroes and asymptotes of an absolute value function-img_0257.jpg
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    Re: Find the domain, zeroes and asymptotes of an absolute value function

    Quote Originally Posted by thebestrose828 View Post
    Hey, I actually finished the problem but I am not sure it's right. I think the horizontal asymptote is at y=0, the vertical asymptotes are at x=3, and x=-3 and xER but x DNE at x=3, -3. I just wanted to check my work with someone because when I tried to find the answer on the calculator, my calculations were different than what the calculator said and I wanted to make sure I had the right answer. I drew out the graph which you will see in the attached image. I will take a picture of what I did and then if someone can just double check to make sure I have it right?
    $y = \dfrac{1}{|x^2-9|^{3/4}}$

    The asymptotes are correct.

    the domain is simply $\mathbb{R}-\{-3,3\}$

    There are no zeros.

    Your graph looks incorrect though.

    Find the domain, zeroes and asymptotes of an absolute value function-clipboard01.jpg
    Last edited by romsek; Jan 8th 2017 at 11:49 AM.
    Thanks from thebestrose828
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    Re: Find the domain, zeroes and asymptotes of an absolute value function

    $y=\dfrac{1}{|x^2-9|^{3/4}}$

    No zeros

    y-intercept is $\left(0,\dfrac{1}{3\sqrt{3}}\right)$

    vertical asymptotes at $x=\pm3$ ... note that the function value increases without bound on both sides of each asymptote.

    horizontal asymptote is $y=0$
    Attached Thumbnails Attached Thumbnails Find the domain, zeroes and asymptotes of an absolute value function-img_1461.png  
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