







A function with 3 asymptotes 
20121019 

From rimoshika: find a function that have 3 Asymptotic : y=x/y=sinx/x=1 Answered by Penny Nom. 





f(x)= (e^x) / [(e^x)+(ex^2)] 
20091110 

From natalie: I'm trying to graph the function, f(x)= (e^x) / (e^x)+(ex^2) [e to the x divided by e to the x plus e times x squared] I know that there aren't any vertical asymptotes, but is there a horizontal asymptote? and also, I'm stuck on finding the concavity for this graph. I tried to find f "(x), but it came out to be really long and I am not sure how to find the x values for f "(x) without using a graphic calculator.
thanks,
natalie Answered by Chris Fisher and Harley Weston. 





Graphing Rational Functions 
20081205 

From Bahra: The question in my homework is: Find all vertical, horizontal, and slant
asymptotes, x and yintercepts, and symetries, and then graph each
function. Check your work with a graphing calculator.
y=3/x+3 meanng: ( y= 3 over x+3) Answered by Janice Cotcher. 





Sketch the graph of the hyperbola and its asymptotes 
20070313 

From Katrina: Given (y2) ^2 – x^2/4 =1 do the following:
Sketch the graph of the hyperbola and its asymptotes. Label the vertices on the graph
I attached the graph thanks for your help! Answered by Penny Nom. 





Vertical asymptotes 
20051205 

From Kelly:
X^{2}  49
Y= 
X^{2} + 9x + 20
We are trying to solve this equation to find the vertical asymptote.
Answered by Penny Nom. 





Asymptotes 
20050606 

From Abraham: What are the equations of all horizontal and vertical asymptotes for the curve y=x/(x(x24))(the answer is y=0, x=2, x=2, but I want to know how to get that algebraically.And why isn't x=0 another asymptote?) Answered by Leeanne Boehm. 





0.999..., asymptotes and infinity 
20041217 

From Mike: My Name is Mike and I teach high school. I had a student ask me to explain why .9 repeating is equal to 1. Then he asked me about an asymptote, or why a parabola or any other curve for that matter can continually approach a value (like 1) and yet never attain a value of 1. He is thinking that these two should represent the same concept and yet they contradict each other. Do you have a solid explanation for him? Of by the way he is a 7th grader. Great little thinker!!!!! Answered by Claude Tardif and Harley Weston. 





A conic 
20040810 

From A student: My question is about this equation 32x*2 18y*2 64x +72y +248 =0
explain why as x goes to the infinity the graph of the conic looks like y= (3/4)X.
What I did to try to find the solution of this problem was to graph and then I thought that maybe trying to find the equation of the asymptotes I could do it, but it was useless because the equation of the asymptotes is y= +4/3(X1) 2 and that does not explain why tho conic looks like y=(3/4) x . I would really appreciate your help on this. Answered by Penny Nom. 





A hyperbola centered at (0,0) 
20011228 

From Carla:
 Find the equation of the hyperbola centered at (0,0) with vertices at (0,3) and (0,3) that is asymptotic to the lines y=+5x.
 Find the equation of a hyperbola in standard position foci (1,5) and (1,7) and eccentricity 2.
Answered by Peny Nom. 





Asymptotes 
20011109 

From Frank:
given the function: f(x) = (x^{2}) / (x1) the correct answer to the limit of f(x) as x approaches infinity is: y = x+1 all math references point to this answer and the method they all use is long division of x1 into x^{2} however if one were to multiply both the numerator and denominator by 1/x and then take the limit, one gets: y=x how can the descrepency between the two answers be explained? Answered by Chris Fisher and Penny Nom. 

