Question about vertical asymptotes

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In summary, a rational function has vertical asymptotes where the denominator is 0, which in this case is at x=3 and x=-1. The horizontal asymptote, at y=1, can be understood by looking at a rough sketch of the function. It is important to note that the signs in the solution for x=3 and x=-1 are not "switched" but rather represent positive and negative values.
  • #1
Johnnycab
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This is a example in my book

a rational function like f(x) = [(x+2)(x-5)]/[(x-3)(x+1)] has vertical asymptotes at x=3 and x=(-1)

Is all you do is switch the addition and subtraction signs in [(x-3)(x+1)]?

The same equation has a horizontal asymptotes at y=1, which i can't seem to understand where it came from

The is the best i could explain this, thank you for reading this
 
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  • #2
Johnnycab said:
The same equation has a vertical asymptotes at y=1, which i can't seem to understand where it came from

Do you mean, a horizontal asymptote? Here, this rough sketch might help: http://archives.math.utk.edu/visual.calculus/1/horizontal.5/index.html" .
 
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  • #3
-sorry iam unable to view the flash pictures, because i can't install macromedia plugin (wont verify)
-could someone give me a written explanation please, iam still lost
 
  • #4
Johnnycab said:
This is a example in my book

a rational function like f(x) = [(x+2)(x-5)]/[(x-3)(x+1)] has vertical asymptotes at x=3 and x=(-1)

Is all you do is switch the addition and subtraction signs in [(x-3)(x+1)]?

The same equation has a horizontal asymptotes at y=1, which i can't seem to understand where it came from

The is the best i could explain this, thank you for reading this

No, you don't ever just arbitrarily "switch signs"! A rational function has vertical asymptotes where the denominator is 0 (and the numerator isn't). The denominator of f(x) is (x-3)(x+1) which equals 0 when x- 3= 0 or x+ 1= 0. To solve x- 3= 0, add 3 to both sides: x- 3+ 3= x= 0+ 3= 3. To solve x+ 1= 0, subtract 1 from both sides: x+ 1- 1= x= 0- 1= -1. See? I didn't "switch signs" anywhere!

I feel I should also point out that the "+" and "-" signs in
x= +3 and x= -1 are not "addition" and "subtraction" signs- they are "positive" and "negative" signs. The difference is subtle but important. (TI calculators have separate "subtraction" and "negative" keys for that reason.)
 
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  • #5
thanks hallsofivy it makes sense now i see what your talking about, thanks for your help
 

1. What is a vertical asymptote?

A vertical asymptote is a line on a graph where the function approaches infinity or negative infinity. It is a vertical line that the graph will never touch or cross.

2. How can you find the vertical asymptote of a function?

To find the vertical asymptote of a function, set the denominator of the function equal to zero and solve for the variable. The resulting value will be the x-coordinate of the vertical asymptote.

3. Can a function have more than one vertical asymptote?

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

4. What does the presence of a vertical asymptote indicate about the function?

The presence of a vertical asymptote indicates that the function is undefined at that particular x-value. This could be due to a division by zero error or an undefined expression.

5. Are vertical asymptotes always straight lines?

Yes, vertical asymptotes are always straight lines that are either vertical or parallel to the y-axis. They can be identified by observing the behavior of the function as x approaches a particular value.

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