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Math Help - Please help! I dont understand oblique asymptotes very well

  1. #1
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    Please help! I dont understand oblique asymptotes very well

    Here's the problem- Sketch the graph of y=f(x)= x^3+x^2-12x.
    Complete the table. x^2-2x-8
    Include all intercepts and asymptotes on the graph.

    Interval
    Test point k
    f(k)
    sign of f
    position of graph

    Here's what I put.
    x-int= (-4,0(3,0)
    y-int= (0,0)
    horizontal asymptote= I'm not sure if this is right, but i got x+3
    vertical asymptote= x=4 x=-2
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  2. #2
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    To find oblique/slant asymptotes, divide the numerator by the denominator. Can you do this?
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  3. #3
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    No not really. Could you help me?
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  4. #4
    MHF Contributor
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    Quote Originally Posted by Jluse7 View Post
    No not really. Could you help me?
    It's very hard to write this kind of division out where you can understand what I mean, so take a look at this page on long division of polynomials. It has really good examples and shows all the steps you need.

    Once you divide the denom. into the numerator, you'll get a line plus a fraction. The fraction will tend to 0 as x gets larger and larger and your function will approach the line more and more.

    Polynomial Long Division: Examples
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  5. #5
    Senior Member I-Think's Avatar
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    Instead of long dividing, you cn use the method of comparing coefficients, it's usually quicker.
    If you have the function
    f(x)=\frac{ax^n+bx^{n-1}+...+c}{dx^m+ex^{m-1}+...+F}
    the it can be written as
    (dx^m+ex^{m-1}+...+F)(gx^{n-m}+...+h)+ix^{n-m}+...+j=ax^n+bx^{n-1}+...+c
    Now compare coefficients
    Question
    \frac{x^3+x^2-12x}{x^2-2x-8}

    (x^2-2x-8)(ax+b)+cx+d=x^3+x^2-12x
    ax^3-2ax^2-8ax+bx^2-2bx-8b+cx+d=x^3+x^2-12x

    Comparing coefficients of x terms
    x^3: a=1
    x^2:b-2a=1
    b=3
    x^1:-8a-2b+c=-12
    c=2
    x^0:-8b+d=0
    d=24
    Last edited by I-Think; November 2nd 2009 at 09:55 AM.
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  6. #6
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    Okay I got that. Now what would you put in for the chart?

    Interval-
    Test Point k-
    f(k)-
    sign of f-
    position of graph-
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