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

1. ## 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.

2. ## Re: Find the domain, zeroes and asymptotes of an absolute value function

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3. ## 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?

4. ## Re: Find the domain, zeroes and asymptotes of an absolute value function

Originally Posted by thebestrose828
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.

$y=\dfrac{1}{|x^2-9|^{3/4}}$
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 $y=0$