Posted by Kenzie on Monday, November 5, 2012 at 11:52pm.
3x1/x^210x+26
Find all (real) zeros of the function
Find all (real) poles of the function
The function has...
A horizontal asymptote at 0?
A nonzero horizontal asymptote?
A slant asymptote?
None of the above

College Algebra  Reiny, Tuesday, November 6, 2012 at 8:30am
I see no = sign in your function, functions are equations.
I see no brackets, but I will assume you mean
f(x) = (3x1)/(x^2  10x + 26)
solving for x^210x+26=0 gives no real roots, so there are no vertical asymptotes
if f(x) = 0, then x=1/3
so the xintercept is 1/3
as x > ∞ , f(x) > 0
so y=0 or the xaxis 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=%283x1%29%2F%28x%5E2++10x+%2B+26%29

College Algebra  Steve, Tuesday, November 6, 2012 at 10:58am
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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