Pre-Cal (Help Plz)

The question I've been trying to figure out is asking me to explain how the graph of (g) is obtained from the graph of (f).

The graphs are as followed:

- f(x)= x^(2)-4

- g(x)= [x^(2)-4]

(Note: the Brackets represent absolute value symbols around the expression for g(x))

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  1. take a look at the graphs and see what you can say.

    And why not use || for absolute value? It's not like you don't have the characters...

    http://www.wolframalpha.com/input/?i=plot+y%3Dx^2-4,+y%3D|x^2-4|

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  2. I looked at the graph and they both look similar. I'm not sure how to put it into the proper words.
    Is there anyway you could explain it to me? I'm having trouble.

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  3. PLEASE

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  4. come on. x^2-4 is negative on the interval (-2,2)

    So, since |x^2-4| is always positive, that little arc below the x-axis is flipped up above it.

    Everywhere else, the two functions are identical.

    g(x) = -f(x) if |x| < 2
    g(x) = f(x) if |x| >= 2

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