Sunday

December 21, 2014

December 21, 2014

Posted by **Kenzie** on Monday, November 5, 2012 at 11:52pm.

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 -
**Reiny**, Tuesday, November 6, 2012 at 8:30amI 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 -
**Steve**, Tuesday, November 6, 2012 at 10:58amodd 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

**Answer this Question**

**Related Questions**

college algebra - Given the following rational function, find a. the horizontal ...

College Algebra - 1.Use completing the square to describe the graph of the ...

college algebra - use rational zeros theorem to find all the real zeros in the ...

college algebra - 1. solve the following logarithmic equation log_8(x+8)+log_8(x...

college algebra - Given the following rational function, find: A. horizontal ...

pre calculus - use the seven step method to graph the following rational ...

Math-precalc - Is it possible to find a rational function that has x-intercepts...

College Algebra - 1.Give a quadratic function q(x) with a vertex of (-1, 2). 2. ...

math help please... - 1.Explain how to find the equation of the vertical ...

Precalculus - Write an equation for rational function with given properties. a...