The range of this function?

**osmosis786** · March 17th 2010, 11:01 AM

The function is f(x)= [6/(x+2)]-3

I wanted to find the range, also could you please post your working as I want to understand how you came to your answer, thanks.

Regards

Ossy

**Anonymous1** · March 17th 2010, 11:09 AM

$f(x)= \frac{6}{x+2}-3$

Where is $f(x)$ undefined? Naturally we look for such things as division by $0.$ When will we have division by $0?$ Clearly when $x+2 = 0,$ $i.e.,$ when $x= -2.$ So $f(x)$ take on all values except when $x = -2.$ What is your range?

**skeeter** · March 17th 2010, 11:21 AM

Originally Posted by osmosis786

The function is f(x)= [6/(x+2)]-3

I wanted to find the range, also could you please post your working as I want to understand how you came to your answer, thanks.

Regards

Ossy

one method of determining the range of a function is to determine the domain of the function's inverse. of course, this depends on whether the inverse exists and is relatively easy to find.

$y = \frac{6}{x+2} - 3$

swap variables ...

$x = \frac{6}{y+2} - 3$

solve for $y$ ...

$x+3 = \frac{6}{y+2}$

$y+2 = \frac{6}{x+3}$

$y = \frac{6}{x+3} - 2$

this is the inverse function ... note that its domain is all real values $x$ such that $x \ne -3$ .

so ... the range of the original function is all real $y$ , $y \ne -3$ .

**Soroban** · March 17th 2010, 12:42 PM

Hello, osmosis786!

When possible, I like to sketch a graph.

Find the range of: . $f(x)\:=\:\frac{6}{x+2} -3$

The graph of . $y \,=\,\frac{1}{x}$ .looks like this:

Code:

                  |
                  |*
                  |
                  | *
                  |  *
                  |    *
                  |           *
    --------------+----------------
      *           |
             *    |
               *  |
                * |
                  |
                 *|
                  |

Domain: . $x\,\neq\,0$
. Range: . $y\,\neq\,0$

The graph of . $y \:=\:\frac{1}{x+2}$
. . is the previous graph moved two units to the left.

Code:

              :   |
              :*  |
              :   |
              : * |
              :  *|
              :   |*
              :   |       *
--------------+---+----------------
  *          -2   |
         *    :   |
           *  :   |
            * :   |
              :   |
             *:   |
              :   |

Domain: . $x\,\neq\,-2$
. Range: . $y\,\neq\,0$

The graph of . $y \:=\:\frac{6}{x+2}$ . rises more "steeply"
. . and "flattens slower", but has the same basic shape.

The graph of . $y \:=\:\frac{6}{x+2} - 3$ . is the previous graph lowered 3 units.

Code:

              :   |
              :*  |
              :   |
              : * |
--------------+--*|--------------
              :   |*
              :   |       *
  - - - - - - o - | - - - - - -
  *        (-2,-3)|
         *    :   |
           *  :   |
            * :   |
              :   |
             *:   |
              :   |

Domain: . $x\,\neq\,-2$
. Range: . $y \,\neq\,-3$

Thread: The range of this function?

LinkBack

Thread Tools

Display

The range of this function?

Similar Math Help Forum Discussions

range of the function

Range of function

Function Range.

Range of a Function

Need the range of this function

Search Tags