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    sarasara's Avatar
    sarasara Posts: 1, Reputation: 1
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    #1

    Jul 1, 2007, 10:58 PM
    functions
    what's the domain and range of f(x)=4/x squared+1 also the x and y intercepts and asymptotes ? As well how do I graph this function?
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Jul 2, 2007, 04:12 AM


    The domain is what you put in and the range is what comes out.

    For the domain, ask yourself, what values can I enter for x and get a valid result?
    Do any entries result in a non-real solutions? Do any entries result in a negative in a square root? Those are normally not viable solutions.

    As for the asymptotes

    horizontal: if the power of the numerator is less than the power of the denominator, then the x-axis is a horizontal asymptote.

    vertical: Are there any values which make the denominator 0? If not, then there is no vertical asymptote.

    For the y-intercept, set x=0 and see what you get. That's the y-intercept.

    For the x-intercepts, the horizontal asymptote will answer that.

    Graph and you can see it.
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