# Thread: Need Help finding range of function with absolute value in denominator

1. ## Need Help finding range of function with absolute value in denominator

I am completely stuck on this question, thanks for all help.

I am supposed to find the domain and range of the function:

$\displaystyle f(x)=\frac{x}{|x|}$

I have solved the domain as $\displaystyle (-\infty,0)\cup(0,\infty)$

It's been quite a few years since I've worked with domain and ranges, then again one with an absolute value in the denominator.

I know that from $\displaystyle (-\infty,0)$ it's a horizontal line at y=-1 and that from $\displaystyle (o,\infty)$ it's a horizontal line at y=1. How do I write the range for this?

2. Originally Posted by jester469
I am completely stuck on this question, thanks for all help.

I am supposed to find the domain and range of the function:

$\displaystyle f(x)=\frac{x}{|x|}$

I have solved the domain as $\displaystyle (-\infty,0)\cup(0,\infty)$

It's been quite a few years since I've worked with domain and ranges, then again one with an absolute value in the denominator.

I know that from $\displaystyle (-\infty,0)$ it's a horizontal line at y=-1 and that from $\displaystyle (o,\infty)$ it's a horizontal line at y=1. How do I write the range for this?
You just wrote it.

3. Originally Posted by dwsmith
You just wrote it.
The range is the y values.

4. Thank you, but how do I write the answer properly? Is it written the same as like a piecewise function?

5. Originally Posted by jester469
Thank you, but how do I write the answer properly? Is it written the same as like a piecewise function?
Yes, that is fine.

6. It's fine how you wrote it. If you wanted to write it in compact form you use set notation,
$\displaystyle R_{f}: \{1\} U \{-1\}$

7. Even more compactly, {1, -1}!

8. $\displaystyle y = \pm 1$

9. lol trust you guys to make a sport of compactness

10. Originally Posted by Krahl
lol trust you guys to make a sport of compactness
... it's a living.

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### range of function with absolute value in denominator

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