How to find out whether a function has vertical asymptotes I got the following question wrong in my exame (16x−64)/(|x|−4) My answer was, -16,16 for the horizontal asymptotes and 4,-4 for the vertical asymptotes. For the horizontal asymptotes the answer is right, But there aren't any vertical asymptotes. I thought if there wasn't a sum of squares in the denominator There would be vertical asymptotes. So I proceeded this way, as I need to equal the denominator to 0 in order to find the vertical asymptotes.

Janiya Rose

Janiya Rose

Answered question

2022-08-10

How to find out whether a function has vertical asymptotes
I got the following question wrong in my exame
  16 x 64 | x | 4
My answer was, -16,16 for the horizontal asymptotes and 4,-4 for the vertical asymptotes.
For the horizontal asymptotes the answer is right, But there aren't any vertical asymptotes.
I thought if there wasn't a sum of squares in the denominator There would be vertical asymptotes.
So I proceeded this way, as I need to equal the denominator to 0 in order to find the vertical asymptotes.
| x | 4 = 0
x−4=0
x=4
−x−4=0
−x=4(−1)
x=−4
There are 3 rules to find the HA's, but what are the rules to find the VA's ?

Answer & Explanation

Rowan Dyer

Rowan Dyer

Beginner2022-08-11Added 14 answers

note that you will have
16 x 64 | x | 4 = 16 ( x 4 ) x 4
if
x 0
or
16 ( x 4 ) x 4
if
x<0

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