# Math Correction

posted by .

Explain how you can tell(without graphing) that the function has no x intercept and no asymptotes. What is the end behaviour?

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 -

Good 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 -

Sorry, there is a correction:
"It is a monotonically increasing function..."
should read
"It is an even function..."

The arguments and conclusions do not change.

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### Math

For homework we're supposed to give all the properties of different functions. I was able to do all of it except for this one greatest integer function - f(x) = -1/2 [x-1] These functions always mess me up! Could someone tell me the …
2. ### Math

Explain how you can tell (without graphing it) that the rational function r(x)= x^6 +10 / x^4+8x^2+15 has no x intercept and no horizontal, vertical, or slant asymptote. What is its end behaviour?
3. ### Pre-Calculus

1) Use a graphing utility to obtain the graph of the function. Give the domain of the function and identify any vertical or horizontal asymptotes. x+4/ x^2+x-6. 2) Use a graphing utility to graph the function and determine the x-intercepts …
4. ### College Algebra HELP

Use the seven step method described in the book to graph the following rational function f(x)=(2x^2+x-3)/(2x^2-7x) 1) Determine the symmetry of the function 2) Find the y-intercept 3) Find the x-intercept 4) Find the vertical asymptotes …
5. ### math help please...

1.Explain how to find the equation of the vertical asymptotes of a reciprocal function. 2.The reciprocal of a linear function and a quadratic function have the same horizontal asymptote. What is its equation?
6. ### math

1.How is the maximum or minimum point of the original quadratic function related to the maximum or minimum point of its reciprocal function?
7. ### math

Given the function f(x)=x^3-2x^2-5x+6/x^2+3x+2 a) Determine algebraically the equation for any asymptotes (HA, VA and or OA) b)State the domain of the function c)State the behaviour of the function at each of the asymptotes
8. ### Math, Algebra, Graphing Systems of Linear Equation

I'm confused about graphing or solving the linear equations for slope/intercept. Here is what I solved: 3x+2y=-6 X-4y=-16 2y= -3x-6 -4y=1x-16 Y=-3/2+3 Y=+1/4+4 ------------- My answer for graphing the systems for the lines to intersect...well, …
9. ### Math, Algebra, Graphing Systems of Linear Equation

I'm confused about graphing or solving the linear equations for slope/intercept. Here is what I solved: 3x+2y=-6 X-4y=-16 2y= -3x-6 -4y=1x-16 Y=-3/2+3 Y=+1/4+4 ------------- My answer for graphing the systems for the lines to intersect...well, …
10. ### Algebra

Graph y=5^x and y=log_5 x on a sheet of paper using the same set of axes. Use the graph to describe the domain and range of each function. Then identify the y-intercept of each function and any asymptotes of each function. So far I …

More Similar Questions