posted by Kenzie on .
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
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
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) = ∞