Math Correction

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

  1. 👍 0
  2. 👎 0
  3. 👁 211
asked by Amanda
  1. 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.

    1. 👍 0
    2. 👎 0
    posted by MathMate
  2. 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.

    1. 👍 0
    2. 👎 0
    posted by MathMate

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

    asked by Mitch n' Joey on December 7, 2017
  2. Pre-Cal

    use a graphing calculator to obtain the graph of the function. What do you observe about its asymptotes? g(x) = 4 [x-2] / x + 1 My answer was there are two horizontal asymptotes. My teacher said that there are two asymptotes but

    asked by Hannah on March 26, 2010
  3. 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

    asked by Rosie on May 15, 2013
  4. Seven step method

    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

    asked by Rosie on May 15, 2013
  5. Pre-Cal

    use a graphing calculator to obtain the graph of the function. What do you observe about its asymptotes? g(x) = 4 [x-2] / x + 1 My answer was there are two horizontal asymptotes but it was wrong.

    asked by Hannah on March 26, 2010
  6. 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

    asked by Addy on April 8, 2011
  7. calculus

    For the function r(x)=x3+6x2x2−36, find the following. a. the y - intercept b. the x - intercepts c. all horizontal asymptotes. y = d. all vertical asymptotes. x =

    asked by Jeffrey on May 29, 2013
  8. Math- Rational Functions

    1. Some rational functions have asymptotes, others have holes, and some have both. Explain how you can identify, without graphing, which graphical features a rational function will have. Can someone explain this thoroughly ? I

    asked by Mae on October 5, 2008
  9. PRE-CALC

    I am given the rational function: f(x)= (x^3 - 1) / (x^2 - 4) I found that the domain is all real numbers except x= plus or minus 2 , I also found that the x intercept is x=1, however I do not get how to find: the y-intercet , or

    asked by KELLIE on September 27, 2017
  10. MATH

    Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label

    asked by MOM on June 9, 2016

More Similar Questions