Sunday

December 21, 2014

December 21, 2014

Posted by **Pamela** on Saturday, July 7, 2007 at 12:08am.

The horizontal asymptote and the x-intercepts parts stump me. If you can't reach y=0, then how can you get the x-intercepts?

And I don't know how to start finding a rational function that has asymptotes x=0 and y=x. It seems like I only have enough space to place a function in Q-2, Q-4.

Well, you can reach y = 0 at x = ±2, but you'll also reach it in the limit x to ± infinity.

You just write down the polynomila that has zeros ar ±2:

x^2 - 4

you divide this by a function whiich has a zero at x = 1: x - 1. You then get:

(x^2-4)/(x-1)

But this function does not go to zero if x goes to infinity. So, you divide this by a polynomial that has no zeroes to make the degree of the denominator larger than the degree of the numerator. You can, e.g. take that polynomial to be x^2 +1. Then you get:

(x^2-4)/[(x-1)(x^2+1)]

And I don't know how to start finding a rational function that has asymptotes x=0 and y=x. It seems like I only have enough space to place a function in Q-2, Q-4."

You can take:

1/x + x

**Answer this Question**

**Related Questions**

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

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

PreCalculus - State the Vertical Asymptote, Horizontal Asymptote, domain, range...

math - Suppose the the limit as x approaches 6 to the left equals infinity. What...

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

College Algebra - Given the following rational functions,find:a.)the horizontal ...

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

Calculus - Which of these rational functions has a ) horizontal asymptote? a ...

math - Give an example of a rational function that has no horizontal asymptote ...

math - There is a vertical asymptote at x=2, and a horizontal asymptote at y=3. ...