Results 1 to 7 of 7

Math Help - Piecewise-Defined Function

  1. #1
    Banned
    Joined
    Jan 2007
    Posts
    315

    Piecewise-Defined Function

    For both questions below:

    (a) Find the domain of the function.

    (b) Locate any intercepts.

    (1)

    .....{3 + x......if -3 <or= to x < 0
    f(x){3...........if......x = 0
    .....{Sqrt{x}..if......x > 0

    =======================

    (2)

    ..........{1/x.........if.....x < 0
    f(x) = {sqrt{x}...if.....x >or= to 0

    NOTE: It is hard to correctly type the piecewise-defined functions using a regular keyboard.

    I hope you can understand the above.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Apr 2006
    Posts
    401
    Quote Originally Posted by symmetry View Post
    For both questions below:

    (a) Find the domain of the function.

    (b) Locate any intercepts.

    (1)

    .....{3 + x......if -3 <or= to x < 0
    f(x){3...........if......x = 0
    .....{Sqrt{x}..if......x > 0

    =======================

    (2)

    ..........{1/x.........if.....x < 0
    f(x) = {sqrt{x}...if.....x >or= to 0

    NOTE: It is hard to correctly type the piecewise-defined functions using a regular keyboard.

    I hope you can understand the above.
    I'll do the first one for you- graph it. The conditions are the "if" parts in the piece-wise function. Domain is (-3, inf) and there are no intersepts. Try graphing it. You have a line with slope = 1 and an exponential function.

    EDIT: Sorry, there are x and y-intercepts, as Soroban pointed out, although the two graphs do not not intersect which is what I was getting at.
    Last edited by AfterShock; January 19th 2007 at 05:01 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,705
    Thanks
    625
    Hello, symmetry!

    For both questions below:
    . . (a) Find the domain of the function.
    . . (b) Locate any intercepts.

    Did you make a sketch?


    (1)\;\;f(x) \:=\:\begin{Bmatrix} 3 + x & &\text{if }\text{-}3 \leq x < 0 \\ 3 & &\text{if }x = 0 \\ \sqrt{x} & &\text{if }x > 0 \end{Bmatrix}
    Code:
                    |
                    |            *
                    *      *
                  * |  *
                *   |*
          ----*-----o--------------
             -3     |
    Domain: . (\text{-}3,\,\infty)

    Intercepts: . (\text{-}3,0),\:(0,3)



    (2)\;\;f(x)\:=\:\begin{Bmatrix}\frac{1}{x} & & \text{if }x < 0 \\ \sqrt{x} & & \text{if }x \geq 0 \end{Bmatrix}
    Code:
                          |
                          |            *
                          |      *
                          |   *
                          |*
        ------------------*----------------
          *               |
                *         |
                     *    |
                       *  |
                        * |
                          |
                         *|
                          |
    Domain: . (-\infty,\,\infty)

    Intercepts: . (0,\,0)

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Jan 2007
    Posts
    315

    ok

    Thank you again both for your quick replies.

    To soroban,

    No, I did not sketch the graph because I do not know how to graph piecewise-defined functions.

    I understand these functions are graphed in parts, right?

    Can you take me through a sample graphing question in terms of this type of function?

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Apr 2006
    Posts
    401
    Quote Originally Posted by symmetry View Post
    Thank you again both for your quick replies.

    To soroban,

    No, I did not sketch the graph because I do not know how to graph piecewise-defined functions.

    I understand these functions are graphed in parts, right?

    Can you take me through a sample graphing question in terms of this type of function?

    Thanks!

    Yes, they are 'graphed in parts,' I guess you could call it.

    For instance,

    Take the first condition;

    f(x) = 3 + x if -3 <= x < 0

    From x = -3 (including this point) to x = 0 (not including, and thus draw an open circle by this point), you will graph 3 + x; see Soroban's graph. The reason why it's closed (solid dot) is because of the next condition later, and thus includes that point. Try look up piece-wise functions on Wikipedia.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Banned
    Joined
    Jan 2007
    Posts
    315

    ok

    I like graphing functions. I think piecewise-defined functions are cool but not easy to sketch.

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,705
    Thanks
    625
    Hello again, symmetry!

    Okay, here's an example.

    . . f(x) \:=\:\begin{Bmatrix}3 & \text{if }0 \leq x \leq 1 \\ 2x + 1 & \text{if }x > 1\end{Bmatrix}


    When x is between 0 and 1 (including the endpoints),
    . . the graph is f(x) = 3, a horizontal line.
    Code:
            |
           3* * * * *
            |
            |
          - + - - - + - -
            |       1

    When x is greater than 1, the graph is f(x) \:=\:2x + 1,
    . . a slanted line.
    Code:
            |
            |                   *
            |                *
            |             *
            |          *
           3|       *
            |
            |
          - + - - - + - - - - - - -
            |       1

    Sketch them on the same graph
    . . and have the graph of the piecewise function.
    Code:
            |
            |                   *
            |                *
            |             *
            |          *
           3o * * * *
            |
            |
          - + - - - + - - - - - - -
            |       1

    This function could be your long-distance charge.

    They might charge $3 for the first minute
    . . and $2 per minute for every subsequent minute.


    (Hmmm, not a good example . . .
    I'm sure someone will point out why.)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. piecewise defined function
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: July 1st 2010, 06:12 AM
  2. Piecewise defined function
    Posted in the Algebra Forum
    Replies: 8
    Last Post: April 20th 2009, 02:25 PM
  3. Piecewise Defined Function
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: December 29th 2008, 09:30 PM
  4. Piecewise-defined Function
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: October 29th 2008, 06:11 PM
  5. piecewise defined function help!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 30th 2007, 08:18 PM

Search Tags


/mathhelpforum @mathhelpforum