Saturday

January 31, 2015

January 31, 2015

Posted by **Amanda** on Wednesday, December 8, 2010 at 7:36pm.

r(x)= x^6+10 / x^4+8x^2+15

How would I solve this? I know it has something to do with factoring but im not sure what else to do.

this is what i have so far:

r(x)= x^6+10 / (x^2+3)(x^2+5)

Can someone help me finish? and explain how the answer? thanks

- Math Correction -
**MathMate**, Wednesday, December 8, 2010 at 7:59pmGood start!

We will examine the numerator, x^6+10.

It is a monotonically increasing function, the minimum value of which is 10 when x=0. So it is non-negative over its domain, ℝ.

The factors of the denominator have similar properties, non-negative throughout its domain, ℝ.

Since the function is a non-negative number divided by a non-negative number, there are no vertical asymptotes, nor does it cross the x-axis.

- Correction -
**MathMate**, Wednesday, December 8, 2010 at 8:35pmSorry, there is a correction:

"It is a monotonically increasing function..."

should read

"It is an even function..."

The arguments and conclusions do not change.

**Answer this Question**

**Related Questions**

Math - Explain how you can tell (without graphing it) that the rational ...

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

Math - For homework we're supposed to give all the properties of different ...

College Algebra HELP - Use the seven step method described in the book to graph ...

Seven step method - Use the seven step method described in the book to graph the...

Pre-Cal - use a graphing calculator to obtain the graph of the function. What ...

Math- Rational Functions - 1. Some rational functions have asymptotes, others ...

math - 1.How is the maximum or minimum point of the original quadratic function ...

asymptotes and graphing, f - how do i identify the asymptotes af the function ...

asymptotes and graphing, f - how do i identify the asymptotes af the function ...