1. ## absolute function

State the domain and range of the following.
$\displaystyle y= \left | 2-\frac{1}{x^2} \right |$

Why is the range greater than or equal to zero? Why isn't it (2, infinity)?

I've just started going through dilations, reflections and translations of different equations and now we are going through absolute functions.

Please show complete working out. All help will be appreciated.

2. Originally Posted by Joker37
State the domain and range of the following.
$\displaystyle y= \left | 2-\frac{1}{x^2} \right |$

Why is the range greater than or equal to zero? Why isn't it (2, infinity)?

I've just started going through dilations, reflections and translations of different equations and now we are going through absolute functions.

Please show complete working out. All help will be appreciated.
I hope you know how the domain is found. Try showing your work if you were unable to find the domain.

Regarding range: Note that there are only positive y-values(absolute function as you have stated). There is no value of x that we can find such that we will get a negative value of y. So, the range for this function is y ≥ 0.

3. Hello, Joker37!

State the domain and range of the following.
$\displaystyle y\:=\: \left| 2-\frac{1}{x^2} \right|$

Why is the range greater than or equal to zero? Why isn't it (2, infinity)?
The graph has $\displaystyle x$-intercepts at: .$\displaystyle \left(\pm\frac{1}{\sqrt{2}},\:0\right)$

The graph of: .$\displaystyle y \:=\:2-\frac{1}{x^2}$ .looks like this:

Code:
                      |
- - - - - - - - - + - - - - - - - - - -
*                2|                 *
*         |           *
--------------o-----+-----o----------------
*   |   *
*  |  *
|
* | *
|
|
*|*
|

The graph of: .$\displaystyle y \:=\:\left|2 - \frac{1}{x^2}\right|$ looks like this:

Code:
                      |
*|*
|
|
* | *
- - - - - - - - - - + - - - - - - - - - -
*              * 2|  *              *
*      *   |   *      *
----------------o-----+-----o----------------
|
|