Can you summarize how to find vertical and horizontal asymptotes and obliques/slants?
Q. Thank you so much for helping me. I know that vertical asymptotes are decided by what makes the denominator equal zero, but I'm still confused about horizontal asymptotes. Thanks in advance!
Asked by # - Fri May 23 18:14:58 2008 - Mathematics - 2 Answers - Comments

A. you will have a horizontal asymptote if the degree of the numerator is ... a. equal to the degree of the denominator .. . . and in that case the asymptote would be the ratio of their highest coefficients also meaning the horizontal asymptote is y = A1/B1 where A1 is the highest coefficient in the numerator , B1 is the highest coefficient in the denominator b. less than the degree of the denominator the horizontal asymptote is y = 0 ... ... ... ... if the degree of the numerator is one more than the degree of the denominator , you have an oblique asymptote the equation is y = Q(x) Q(x) = quotient when the numerator is divided by the denominator .. . .. .
Answered by Alam Ko Iyan - Fri May 23 21:25:32 2008

What are the Vertical and horizontal asymptotes of this function?
Q. What are the Vertical and horizontal asymptotes of the function h(x) = (2x - 12) / (x + 4)??? how do i do this someone please show me step by step..!!! And also what are the x- intercept and y- intercept of this function?
Asked by - Tue Dec 1 13:38:26 2009 - Mathematics - 1 Answers - Comments

A. for vertical, set the denominator equal to zero for horizontal, use this rule regarding the x powers: same, divide the coefficients. this is what you'll use upper x is larger (squared, etc) then slant asymptote forgot what happens if the lower is larger
Answered by Jo M - Tue Dec 1 13:46:23 2009

Find the vertical and horizontal asymptotes of this exponential function ?
Q. I need help finding the vertical and horizontal asymptotes of this function . f(x) = e ^ - ( ( x^2 - 2x + 1 ) / 2 ) Thanks in advance.
Asked by - Wed Nov 24 10:52:03 2010 - Mathematics - 1 Answers - Comments

A. This function has no vertical asymptotes. Horizontal asymptote is the x axis as when x is very large and positive, f(x) is approaching zero.
Answered by mathsmanretired - Wed Nov 24 11:19:43 2010

How to find vertical and horizontal asymptotes?
Q. I need to find all vertical and horizontal asymptotes of the graph of the given function: f(x) = (5x^2)/(x^2-3x-4) If you could show me how this is done, that would be great. Thanks!
Asked by devzor - Tue Jul 13 13:16:14 2010 - Mathematics - 1 Answers - Comments

A. Vertical asymptotes are found where the denominator equals zero... x2 - 3x - 4 (x - 4)(x + 1) x = 4, -1 There are two vertical asymptotes, x = -1 and x = 4 To find horizontal asymptotes, look at the highest order term in the numerator and denominator, if they are the same, then the horizontal asymptote is the leading coefficient of the numerator over the leading coefficient of the denominator... 5x2 / x2 - 3x - 4 5 / 1 The horizontal asymptote is y = 5 If there is bigger exponent in the denominator of the equation or function, the x-axis will yield the horizontal asymptote. If there is a bigger exponent in the numerator of a given equation or function, then there is NO horizontal asymptote whatsoever.
Answered by - Tue Jul 13 14:28:12 2010

How do I find the vertical and horizontal asymptotes of rational functions that have a numerator and denominat?
Q. How do I find vertical and horizontal asymptotes of rational functions that have a numerator and denominator with the same degree. Please use this example to show me: f(x) = (2x^2-8) / ((2x-9) (x+2))
Asked by captainamazing - Fri Nov 25 23:35:32 2011 - Mathematics - 1 Answers - Comments

A. Vertical asymptotes occur when the denominator is equal to 0 0 = (2x - 9) * (x + 2) 2x - 9 = 0 2x = 9 x = 9/2 x + 2 = 0 x = -2 x = -2 , 9/2 Horizontal asymptotes describe the end behaviors of a function. In this case, we can reduce the fraction: (2x^2 - 8) / ((2x - 9) * (x + 2)) => 2 * (x^2 - 4) / ((2x - 9) * (x + 2)) => 2 * (x - 2) * (x + 2) / ((2x - 9) * (x + 2)) => 2 * (x - 2) / (2x - 9) => (2x - 4) / (2x - 9) => (2x - 9 + 5) / (2x - 9) => (2x - 9) / (2x - 9) + 5 / (2x - 9) => 1 + 5 / (2x - 9) What happens as x goes to negative infinity? 1 + 5 / (-inf - 9) => 1 + 5 / (-inf) => 1 + 0 => 1 What happens as x goes to positive infinity? 1 + 5 / (inf - 9) => 1 + 5 / inf => 1 + 0 => 1 So the horizontal… [cont.]
Answered by Captain Matticus, LandPiratesInc - Fri Nov 25 23:48:33 2011

Find the vertical and horizontal asymptotes of this equation help please?
Q. (x)^2/x^2-1x-12 find the vertical and horizontal asymptotes
Asked by - Wed Dec 14 00:26:02 2011 - Mathematics - 1 Answers - Comments

A. y = x^2/(x^2 - x - 12) horizontal: y = 1 vertical: (x + 3)(x - 4) = 0 x = -3 x = 4
Answered by iceman - Wed Dec 14 00:29:52 2011

what are the vertical and horizontal asymptotes of f(x)= x^3-3x^2+3?
Q. I know finding asymptotes is pretty basic, but can someone show me the steps how to find them? I have a feeling that there are no vertical or horizontal asymptotes for this function at all. But if I'm wrong help will be greatly appreciated.
Asked by Roshelle - Wed Dec 22 18:05:38 2010 - Mathematics - 3 Answers - Comments

A. There isn't any vertical or horizontal asymptotes. This is because lim (x-->-infinity) f(x) and lim (x-->infinity) f(x) are both non-existent (with means no horizontal asymptotes) and f(x) is continuous for all real x (which rules out vertical asymptotes). I hope this helps!
Answered by - Wed Dec 22 18:18:16 2010

How to find horizontal asymptotes?
Q. The graph of the function f(x) = (x+1) / (x^2 +3x - 4) has a horizontal asymptote. If the graph crosses this asymptote, then give the x-coordinate for the intersection. Otherwise state that the graph does not cross the asymptote. Idk how to do this. Do I have to set them equal to each other because they are intersecting?? Thank you to anyone who would help me.
Asked by ENiGMATiCGiRL - Fri Aug 27 21:37:13 2010 - Mathematics - 1 Answers - Comments

Determine the equation of a rational function without any holes, vertical asymptotes or horizontal asymptote?
Q. could anyone help me with one of the two questions??? Determine the equation of a rational function without any holes, vertical asymptotes or horizontal asymptote? identify a rational function whose graph has the horizontal asymptote y=2 and two vertical asymptotes?
Asked by - Sun Mar 6 14:30:12 2011 - Mathematics - 2 Answers - Comments

A. 1.) The graph y = x is sufficient. No asymptotes, no holes, and rational. 2.) Consider the graph of y = 1/x. This has a vertical and horizontal asymptote along both axes. To move the horizontal asymptote to y=2, we merely need to translate our graph two units up, thus we need the graph of y = 1/x + 2. However, we need two vertical asymptotes, and as such we need two values for which the denominator is not defined. This is easily done by altering our function to [ 1/(x2 - 16) ] + 2, so that we get vertical asymptotes at x = 4 and x = -4. (Of course the value 16 here is arbitrary, we could take any positive value to be subtracted.)
Answered by Daniel C - Sun Mar 6 14:43:26 2011

What are the vertical asymptotes & horizontal asymptotes of this function?
Q. Can somebody help me please, function is below: What are the vertical asymptotes & horizontal asymptotes of this function?
Asked by - Tue Nov 9 13:23:04 2010 - Mathematics - 1 Answers - Comments

A. f(x) = (x2 + 4x + 4) / (x2 - 5x - 6) vertical asymptotes: x2 - 5x - 6 = 0 x = -1 and x = 6 horizontal asymptote: degree of denominator is greater than numerator, so y = 0
Answered by I'm with Stupid - Tue Nov 9 15:20:24 2010

What are the equations of the vertical and horizontal asymptotes of this function?
Q. By using limits, what are the equations of the vertical and horizontal asymptotes of this function: f(x) = (2x+1)/x show your work please, thanks in advance!
Asked by Samantha - Tue Nov 10 15:41:32 2009 - Mathematics - 3 Answers - Comments

A. Because Lim of f(x) for x->0 + = +infinity and Because Lim of f(x) for x->0 - = - infinity Then x = 0 equation of vertical asymptote Because Lim of f(x) for x-> +infinity = 2 and Because Lim of f(x) for x-> - infinity = 2 THen y = 2 horizontal asymptote
Answered by Moise Gunen - Tue Nov 10 15:53:09 2009

How do I find the horizontal asymptotes for the following?
Q. How do I find the horizontal asymptotes for the following? f(x) = 5x^3-2x^2+1/4x^3+2x-7 Is the answer 5/3? 5/4? or 5/5? Please be show details.
Asked by df x - Thu Feb 12 01:42:22 2009 - Mathematics - 2 Answers - Comments

A. To find the horizontal asymptote, set the denominator equal to zero. After setting this to zero, then simply solve for the "x." This is how you find the horizontal asymptote.
Answered by Pointy - Thu Feb 12 02:05:11 2009

How do I calculate the horizontal/oblique asymptotes of the function f(x)=xe^x?
Q. From my graphing calculator I believe that the horizontal asymptote is y=0, but I have no idea of how to prove it algebraically.
Asked by ying - - Fri Jul 30 23:23:31 2010 - Mathematics - 2 Answers - Comments

A. What tools do you have at your disposal? If you can use limits, you can use that fact that lim( x -> - ) xe^x = lim( u -> ) -u e^(-u) = lim( u -> ) -u/e^(u) = 0 which you can show by using L'Hopital's rule or by appealing to the Maclaurin series for the exponential. So y = 0 is a horizontal asymptote to the graph of f. There are no oblique asymptotes to the graph of f and no other horizontal asymptotes. *** Update *** The limit at negative infinity is zero. Double check this.
Answered by Lake R - Fri Jul 30 23:30:33 2010

Is 3 the correct answer for this question about horizontal asymptotes?
Q. (3x^3-7x^2+2)/(5x^3-11x) i was asked to find the horizontal asymptote and i got y=3/1 is this correct? if not, whats the answer?
Asked by Kat D - Fri Jun 19 01:06:39 2009 - Mathematics - 2 Answers - Comments

A. y=3/5 is hor asy.
Answered by nozar nazari - Fri Jun 19 01:14:05 2009

How do you find Vertical and Horizontal asymptotes of a rational function using TI-84 calculator?
Q. How would you use the graphing calculator to find the Vert. and Hort. asymptotes of (3x^2+x-4) / (2x^2-5x) ? I know that you can put the function in and look at the graph visually. But is there way to find the asymptotes on the graphing calculator if the answer is not an obvious whole number like -4/3.
Asked by - Sun Aug 29 16:50:21 2010 - Mathematics - 1 Answers - Comments

A. you dont need a calc to fig out the asymptotes.. Just solve for X in the equation and figure out the asymptotes example x2 5x 6 = 0 (x 6)(x + 1) = 0 x = 6 or 1 So x cannot be 6 or 1, because then I'd be dividing by zero.
Answered by Vye Brator - Sun Aug 29 19:51:08 2010

Does the sine function have horizontal asymptotes?
Q. When graphing the sine function, does it have horizontal asymptotes or not?
Asked by randomsounds - Sun Apr 12 16:32:53 2009 - Mathematics - 2 Answers - Comments

A. The definition for asymptote is given in the link below. As the independent variable x tends to infinity, the function f(x) , if it has an asymptote, will get closer and closer to the asymptote but not actually reach it . In the case of a sine curve, there is no such asymptote, since the two bounds namely -1 and +1 set the limit for the sine graph but does not make it closer and closer to +1 or to -1. It is said to oscillate between +1 and -1 and does not converge to +1 or -1.
Answered by rk - Sun Apr 12 16:45:22 2009

Can you find find all vertical and horizontal asymptotes?
Q. Find all vertical and horizontal asymptotes: y= (2x-5) / (x+4) My answers were... vertical asymptote = - 4 and horizontal asymptote = 2 I'm not sure about my answer so I was hoping you guys could tell me what you get. Thank you very much!
Asked by strikexaxpose93 - Sat Jun 26 23:53:16 2010 - Mathematics - 3 Answers - Comments

A. I got the same answer as you! Good job.
Answered by - Sat Jun 26 23:57:08 2010

How do you tell how many horizontal asymptotes a function has?
Q. Say, y=x^2/(x^2-1), i know how to tell where the vertical ones are, just not horizontal, I know that it has 2 vertical. Please tell me how to determine the horizontal... Thanks!!!
Asked by - Sun Apr 10 17:18:06 2011 - Mathematics - 2 Answers - Comments

A. 1. The answer is 1/2 - look at the numerator and denominator (values associated with x) ie 2x, 3x^2 2. If the numerator denominator, then there's no horizontal asymptote.
Answered by - Sun Apr 10 17:21:45 2011

How do I determine the vertical and horizontal asymptotes of the graph of the given function?f(x) = ( x^2 - 1?
Q. How do I determine the vertical and horizontal asymptotes of the graph of the given function? In addition, it asks to sketch the graph and determine the appropriate WINDOW values. Please help. f(x) = ( x^2 - 1 ) / ( x + 2)
Asked by - Wed May 4 14:12:15 2011 - Mathematics - 1 Answers - Comments

A. Vertical asymptote when function is undefined Undefined when denominator = 0 (x+2) = 0 x = -2 (is a vertical asymptote) Horizontal asymptotes only occur y = 0 if the highest power in denominator is greater than highest power in numerator. (ie. x/x2 means asymptote at y = 0) y = ratio of coefficients if the highest powers in numerator and denominator are the same (ie. 3x2/5x2 means an asymptote at y = 3/5) NO horizontal asymptote if the highest x power in the numerator is greater than the highest x power in denominator (ie. x2/x means NO Horizontal asymptote) <--- This is the case for your problem.
Answered by hsueh010 - Wed May 4 14:17:27 2011

Use limits to find the equations of all the vertical and horizontal asymptotes?
Q. . For each given function a) Determine the values of x where the function is not continuous. b) Use limits to find the equations of all the vertical and horizontal asymptotes I) g(x)=x^2-9/x-3 II) r(x)=2x^2+10x/x^2+4x-5
Asked by MO - Mon Jun 7 07:56:50 2010 - Mathematics - 1 Answers - Comments

A. a. Will have a discontinuity at x = 3 (denominator = 0). The expression simplifies to g(x) = x + 3, so the graph is a straight line with the discontinuity at x = 3 b. r(x) = 2x(x + 5)/(x + 5)(x - 1) so it will have vertical asymptotes at -5 and 1. to find the horizontal asymptotes using limits, take the limit as x ===> inf of r(x) = lim 2x/(x - 1) = lim 2/(1 - 1/x) (mult num and denom by 1/x) = 2
Answered by - Tue Jun 8 09:12:01 2010