1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Domain of a Function with Sign Graph

  1. Aug 26, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the domain of the function. You will need a sign graph. Answer in interval notation.


    2. Relevant equations

    f(x)= (3)/[(x2-4x)1/2]



    3. The attempt at a solution
    No clue - I don't know how to use a sign graph or what the positive/negative results mean as solutions on a number line.
     
  2. jcsd
  3. Aug 26, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    I am not sure what a sign graph is.

    But the domain is the x values for f being defined. There is a square root, so what is inside can't be less than zero. Since it is a fraction, the denominator can't be zero.
     
  4. Aug 26, 2009 #3
    Sine graph?
     
  5. Aug 27, 2009 #4
    I meant sine graph instead of sign graph. So what do I do? Should I set the denominator to greater than or equal to zero and solve?

    I tried solving using the above method but I think my math is wrong. Nonetheless it is wrong because my teacher wants a sine graph on a number line...

    1) (sqrt(x2-4x) greater than or equal 0
    2) x2-4x greater than or equal 0 (this step is wrong I'm pretty sure - squaring both sides)
    3) x2-4x+4 greater than equal 4
    4) (x-2)2 greater than equal 4

    .... ? I still need the sine graph.
     
  6. Aug 27, 2009 #5
    I suspect "sign graph" was the correct original intent.

    When solving [itex]x^2-4x = x(x-4) > 0[/itex], this boils down to the cases:

    [tex]\left\{ \begin{array}{r}{ x > 0 \\ x-4<0} \end{array}[/tex]

    [tex]\left\{ \begin{array}{rl} {x<0 \\ x-4 >0} \end{array}[/tex]

    This can also be illustrated with a sign graph of x^2 - 4x:

    + + + + + + + + + + + - - - - - - + + + + + + + + +
    ___________________0________4________________

    And from this one can determine the domain...

    Solving [itex](x-2)^2 > 4 \Rightarrow |x-2| > 2[/itex] is also valid.

    --Elucidus

    EDIT: Fixed a TeX gaffe.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Domain of a Function with Sign Graph
  1. Domain of a function (Replies: 7)

  2. Domain of a Function (Replies: 2)

Loading...