Results 1 to 4 of 4

Thread: The range of this function?

  1. #1
    Junior Member
    Joined
    Mar 2009
    Posts
    28

    Exclamation The range of this function?

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1
    $\displaystyle f(x)= \frac{6}{x+2}-3$

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

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,216
    Thanks
    3702
    Quote Originally Posted by osmosis786 View Post
    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.

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

    swap variables ...

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

    solve for $\displaystyle y$ ...

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

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

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

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

    so ... the range of the original function is all real $\displaystyle y$ , $\displaystyle y \ne -3$.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    849
    Hello, osmosis786!

    When possible, I like to sketch a graph.


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

    The graph of .$\displaystyle y \,=\,\frac{1}{x}$ .looks like this:
    Code:
                      |
                      |*
                      |
                      | *
                      |  *
                      |    *
                      |           *
        --------------+----------------
          *           |
                 *    |
                   *  |
                    * |
                      |
                     *|
                      |
    Domain: .$\displaystyle x\,\neq\,0$
    . Range: .$\displaystyle y\,\neq\,0$



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

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



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



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

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

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

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. range of the function
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Mar 30th 2010, 06:19 AM
  2. Range of function
    Posted in the Pre-Calculus Forum
    Replies: 9
    Last Post: Jan 18th 2010, 05:22 AM
  3. Function Range.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Jul 28th 2009, 07:26 PM
  4. Range of a Function
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: Oct 2nd 2008, 02:01 PM
  5. Need the range of this function
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 6th 2008, 06:40 PM

Search Tags


/mathhelpforum @mathhelpforum