College Algebra

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3x-1/x^2-10x+26
Find all (real) zeros of the function
Find all (real) poles of the function
The function has...
A horizontal asymptote at 0?
A non-zero horizontal asymptote?
A slant asymptote?
None of the above

  • College Algebra -

    I see no = sign in your function, functions are equations.

    I see no brackets, but I will assume you mean

    f(x) = (3x-1)/(x^2 - 10x + 26)

    solving for x^2-10x+26=0 gives no real roots, so there are no vertical asymptotes
    if f(x) = 0, then x=1/3
    so the x-intercept is 1/3
    as x ---> ∞ , f(x) ---> 0
    so y=0 or the x-axis is a horizontal asymptote
    (from above for positive x's , from below for negative x/s
    there is no slant asymptote

    I don't know what you mean by "poles"

    Here are two graphs of your function by Wolfram
    http://www.wolframalpha.com/input/?i=%283x-1%29%2F%28x%5E2+-+10x+%2B+26%29

  • College Algebra -

    odd to be using the term "pole" which is usually reserved for functions of a complex variable. Here it is apparently used to indicate a vertical asymptote, since for a complex function

    f(z), a pole at z=c means

    lim f(z) = ∞
    z→c

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