College Algebra
posted by Kenzie .
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
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
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
Respond to this Question
Similar Questions

Precalculus
Write an equation for rational function with given properties. a) a hole at x = 1 b) a vertical asymptote anywhere and a horizontal asymptote along the xaxis c) a hole at x = 2 and a vertical asymptote at x = 1 d) a vertical asymptote … 
College Algebra
1.Use completing the square to describe the graph of the following function. Support your answer graphically. f(x) = 2x^2 + 4x + 5 2. Find the vertical, horizontal, and oblique asymptotes, if any, for the following rational function. … 
algebra
find the slant asymptote of the graph of the rational function and use the slant asymptote to graph. f(x)=x^2+x2/x7 find slant asymptote of graph of f use slant asymptote to graph rational function find x and y intercepts find vertical … 
college algebra
Given the following rational function, find: A. horizontal asymptotes B. vertical asymptote(s), if any C. oblique asymptote(s), if any f(x)=x^2x2/2x^2x21 
college algebra
Given the following rational function, find a. the horizontal asymptote(s), b. the vertical asymptote(s), if any, and c. the oblique asymptote(s), if any. f(x)=(x^2x2)/(2x^2x10) 
College Algrbra
Given the following rational function, f(x)=x^2x2/ax^2x21 find (a) the horizontal asymptote(s) (b) the vertical asymptote(s), if any and (c) the oblique aasymptote(s) if any 
pre calculus
use the seven step method to graph the following rational function: f(x)=3x^2+x4/2x^25x a. determine the symmetry of the function. b. find the x and y intercepts. c. find the verticle asymptote d.find the horizontal asymptote e.plot … 
Math
Write a rational function satisfying the following criteria. vertical Asymptote: x=1, slant asymptote: y=x+2, zero of the function: x=3 I had f(x)=x^2+3x+2/x+1, that only works for the asymptotes and not the zero can someone please … 
Math
What is the:  vertical asymptote horizontal asymptote non permissible value of y=(x^2+x12)/(x+4) ? 
Math (Integrals)
The area A between the graph of the function: g(t) = 4  (4/t^2) and the taxis over the interval [1, x] is: A(x) = ∫[1, x] (4  (4/t^2)) dt a) Find the horizontal asymptote of the graph g. I believe the horizontal asymptote of graph …