Describing behavior on each side of a vertical asymptote

In summary, the vertical asymptotes of the graph of F(x) = (3 - x) / (x^2 - 16) are x = 4 and x = -4. The behavior of f(x) as it approaches these asymptotes is as follows: f(x) approaches +inf as it approaches x = -4 from the left, f(x) approaches -inf as it approaches x = -4 from the right, f(x) approaches +inf as it approaches x = 4 from the left, and f(x) approaches -inf as it approaches x = 4 from the right. This can be determined using limits.
  • #1
Jacobpm64
239
0
Find the vertical asymptotes of the graph of F(x) = (3 - x) / (x^2 - 16)

ok if i factor the denominator.. i find the vertical asymptotes to be x = 4, x = -4.

The 2nd part of the problem asks:
Describe the behavior of f(x) to the left and right of each vertical asymptote.. I'm not sure what i need to write for this.
 
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  • #2
It's asking for what happens as the function appraches the asymptotes from the left and the right, does it go to infinity - what?

You can use limits to find out.
 
  • #3
ahh thanks.. so...

f(x) approaches +inf as it approaches x = -4 from the left...
f(x) approaches -inf as it approaches x = -4 from the right...
f(x) approaches +inf as it approaches x = 4 from the left...
f(x) approaches -inf as it approaches x = 4 from the right...

correct?
 
  • #4
Correct. :smile:
 

What is a vertical asymptote?

A vertical asymptote is a vertical line on a graph that represents a value where the function approaches but never touches. It can also be thought of as a boundary or limit for the function.

What does it mean for a function to have a vertical asymptote?

If a function has a vertical asymptote, it means that the function is undefined at that particular value. This can happen when the denominator of a rational function becomes zero.

How do you describe behavior on each side of a vertical asymptote?

The behavior on each side of a vertical asymptote can be described using limit notation. For example, if the asymptote is located at x=a, the limit of the function as x approaches a from the left side would be written as lim x→a- f(x) and the limit from the right side would be written as lim x→a+ f(x).

What are the different types of behavior on each side of a vertical asymptote?

There are three types of behavior that can occur on each side of a vertical asymptote: approaching from above, approaching from below, and approaching from opposite directions. The type of behavior depends on the slope and the concavity of the function.

How can I use the behavior on each side of a vertical asymptote to analyze a function?

By understanding the behavior on each side of a vertical asymptote, we can determine the end behavior of a function and identify any discontinuities. This can help us graph the function accurately and make predictions about its behavior. It is also useful for finding limits of the function.

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