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Math Help - Domain +Graphing

  1. #1
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    Domain +Graphing

    I need to determine the domain, sketch the graph of each function and show/explain the connection between the graph and the domain:


    g (x) = x^2
    ______________

    x^2 + 2x - 3
    x^2 + 2x-3 should be greater than 0 since (Any number)/0 is NOt Defined

    (X+3)(X-1)>0
    So either
    X> -3 OR X>1

    Thus domain becomes
    (-3,1)u(1,Infinity)

    Right?

    Now how wld I graph and explain the connection??
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by askmemath
    x^2 + 2x-3 should be greater than 0 since (Any number)/0 is NOt Defined

    (X+3)(X-1)>0
    So either
    X> -3 OR X>1

    Thus domain becomes
    (-3,1)u(1,Infinity)

    Right?

    Now how wld I graph and explain the connection??
    The values of x such that x^2+2x-3=0 are forbidden. NOT where x^2+2x-3 is negative. There are three parts to the domain.

    Wherever the denominator goes to zero will be a vertical asymptote (unless the numerator also goes to zero at this value of x, which does not happen here).

    -Dan
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  3. #3
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    Quote Originally Posted by topsquark
    The values of x such that x^2+2x-3=0 are forbidden. NOT where x^2+2x-3 is negative. There are three parts to the domain.

    Wherever the denominator goes to zero will be a vertical asymptote (unless the numerator also goes to zero at this value of x, which does not happen here).

    -Dan
    Umm, So the domain becomes....??

    And how would I be graphing this?
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  4. #4
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    Quote Originally Posted by askmemath
    Umm, So the domain becomes....??
    The domain is that "x" can be any number EXCEPT -3,1.

    You can write it in three ways,
    x\in \mathbb{R}, x\not = -3,1
    Or,
    \left\{ \begin{array}{c}x<-3\\ -3<x<1\\ 1<x
    Or,
    x\in (-\infty,-3)\cup (-3,1) \cup (1,+\infty)
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  5. #5
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    Quote Originally Posted by askmemath
    And how would I be graphing this?
    Step 1 draw vertical line which are asymptotes for the undefinied values. That means draw x=-3,x=1

    Step 2 find how f(x) behaves as you approach one of these values from the left and right. Meaning, begin with the vertical asymptotes x=-3 first. As you approach the number -3 from the left what happens to f(x)? It gets bigger and bigger. That means it is approaching +infinity so you approach the asymptote line but you never pass it. Next what happens when you approach x=-3 from the left? It gets smaller and smaller. That means it is approaching -infinity so you approach the asymptote line but you never pass it and go down. The same approach use for x=1.
    Attached Thumbnails Attached Thumbnails Domain +Graphing-picture4.gif  
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