Finding Vertical Asymptotes: Graphing (x-1)/(1-x^2) | Step-by-Step Tutorial

Therefore, the vertical asymptotes occur at x=1 and x=-1.In summary, the graph of (x-1)/(1-x^2) has vertical asymptotes at x=1 and x=-1.
  • #1
TrueStar
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0

Homework Statement



Sketch the graph of (x-1)/(1-x^2).


Homework Equations



Vertical Asymptotes are found in the denominator.


The Attempt at a Solution



I have all I need to sketch this graph except the vertical asymptote. The 1-x^2 is throwing me off. I thought it would come out as a difference of squares, but this can also be -x^2+1.
 
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  • #2
The vertical asymptote occurs where the denominator goes to zero.
Where does the function 1 - x^2 become zero?

I don't really understand your last remark. You think that 3 - 5 is something else than -5 + 3?
 
  • #3
Yes, and trying to solve for zero is confusing me. 1-x^2 is the same as -x^2+1. If I move the 1 over, I'll get -x^2=-1 and I don't want negative square roots.

Just looking at it, I think it should be 1 and -1, but I want to show my work.
 
  • #4
TrueStar said:
If I move the 1 over, I'll get -x^2=-1 and I don't want negative square roots.

You're thinking too hard

-x^2=-1 doesn't have any negative square roots, does it? :wink:

get some sleep! :zzz:​
 
  • #5
*headdesk* Nooo... it does not have negative square roots. :frown: How embarrassing.

In my defense, I've been using my weekend to study for my college algebra exam, memorize polyatomic ion names, and prepare to give a speech about the wonderful world of autoclaves.

Is there a point where one can study too much? I think I'll finish this problem up and take a break. Thank you both. :)
 
  • #6
TrueStar said:
… autoclaves.

mmm … too much pressure! :rolleyes:
 
  • #7
tiny-tim said:
You're thinking too hard

-x^2=-1 doesn't have any negative square roots, does it? :wink:

get some sleep! :zzz:​

Equivalently, x^2 = 1, which has two roots, one of which is negative.
 

1. What is the definition of a vertical asymptote?

A vertical asymptote is a vertical line on a graph where the function approaches infinity in either the positive or negative direction. It can also be defined as a value of x for which the function is undefined.

2. How do I find the vertical asymptotes for a given function?

To find the vertical asymptotes for a function, set the denominator equal to zero and solve for x. The resulting values of x will be the vertical asymptotes.

3. Can a function have multiple vertical asymptotes?

Yes, a function can have multiple vertical asymptotes. This occurs when there are multiple values of x that make the denominator of the function equal to zero.

4. How do I graph a function with vertical asymptotes?

To graph a function with vertical asymptotes, plot the vertical asymptotes as dotted lines on the graph. Then, plot points on either side of the asymptotes to show the behavior of the function as it approaches the asymptotes.

5. Is (x-1)/(1-x^2) a rational function?

Yes, (x-1)/(1-x^2) is a rational function. A rational function is defined as a function that can be expressed as the ratio of two polynomials, and this function fits that criteria.

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