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Math Help - Sketching a Graph

  1. #1
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    Sketching a Graph

    Short of using my calculator how do I go about finding out all the transition points, asymptotes and intercepts of an equation?

    y= __1_
    x2+3
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Sketching a Graph

    a) I am assuming transition points refer to local extrema (or other potential places the slope changes sign) and inflections points.

    i) local extrema:

    Equate the first derivative to zero, solve for x.

    ii) places where function is not differentiable:

    Look at where the derivative is undefined or does not exist.

    iii) inflection points:

    Equate the second derivative to zero to find critical numbers, and check to see if the sign of the second derivative changes across these critical numbers.

    b) asymptotes

    i) vertical:

    look at where the function is undefined, and ensure the singularity in not removable.

    ii) horizontal:

    Evaluate \lim_{x\to\pm\infty}f(x).

    iii) oblique

    If the degree of the numerator is one more than the degree of the denominator, perform polynomial division and the quotient gives the asymptote.

    c) intercepts

    i) x

    Set f(x)=0 and solve for x.

    ii) y

    Evaluate f(0).
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