How Do I Find the Asymptotes of a Function?

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In summary, the conversation discusses finding the asymptotes of a given function using graphing strategies. The problem involves checking for various values such as domain, intercepts, critical values, and intervals of increase and decrease. The process of finding horizontal asymptotes is explained, and it is mentioned that for vertical asymptotes, one must find where the function goes to infinity. The conversation ends with a question about the meaning of "k."
  • #1
donjt81
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ok so i have this problem where i am asked to find the asymptotes. It is kinda throwing me off because it is in the middle of the differentiation section. so here is the problem

problem: use the graphing strategy to sketch the graph of y=(4x)/(x^2+1). check for domain values, intercepts, asymptotes, critical values, interval where the function is increasing and where it is decreasing, intervals where it is concave up and where it is concave down. Then graph it. please use sign charts.

I have done all the other stuff but I don't know how to find the asymptotes. Can someone help please.
 
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  • #2
To find the horizonal asmptotes, you need to first factor the f(x) or y function (already done in your case), and then look at the co-efficients of the largest power of x in the numberator and denominator. [tex]f(x) = ax^m / bx^k[/tex]. Then if
1.m < k, the asymptote is at y= 0.
2. m = k, the asymptote is at a/b
3. m > k, there is no asymptote

For vertical asymptotes, you need to find where the function goes to infinity (i.e. the value of x for which the denominator equals zero). I'm not sure what a complex asymptotes means.
 
Last edited:
  • #3
what is k?
 
  • #4
Just edited it, n = k.
 

Related to How Do I Find the Asymptotes of a Function?

What is an asymptote?

An asymptote is a line that a curve approaches but never touches. It can be either horizontal, vertical, or oblique.

How do I find the asymptotes of a function?

To find the asymptotes of a function, you need to first simplify the function and then look for any restrictions on the domain. Horizontal asymptotes can be found by taking the limit as x approaches positive or negative infinity. Vertical asymptotes occur when the denominator of a fraction approaches 0.

What is the difference between a removable and non-removable asymptote?

A removable asymptote is a type of vertical asymptote where the function can be simplified to remove the asymptote. A non-removable asymptote is a vertical asymptote that cannot be simplified and is a permanent part of the function.

Do all functions have asymptotes?

No, not all functions have asymptotes. Only certain types of functions, such as rational functions, have asymptotes.

How can I use asymptotes to help graph a function?

Asymptotes can help you determine the behavior of a function as x approaches infinity or negative infinity. They can also help you identify any restrictions on the domain of the function. By plotting the asymptotes on a graph, you can get a better understanding of the overall shape of the function.

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