How to find a if the function below doesn't have a vertical asymptotes. f(x)=(x2−ax+2)/(x−2)

kadejoset 2022-07-23 Answered
Asymptotes of function
How to find a if the function below doesn't have a vertical asymptotes.
f ( x ) = x 2 a x + 2 x 2
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Answers (2)

penangrl
Answered 2022-07-24 Author has 17 answers
A function like that has vertical asymptote when it's denominator is 0, that happens when x=2
f ( x ) = x 2 a x + 2 x 2
But since we don't want f(x) to have a vertical asymptotes, then x−2 must be a factor of x 2 + a x + 2
x 2 a x + 2 = ( x 2 ) ( x b )
6 2 a = 0
f ( x ) = x 2 3 x + 2 x 2
f ( x ) = ( x 2 ) ( x 1 ) x 2
f ( x ) = ( x 1 )
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Haley Madden
Answered 2022-07-25 Author has 7 answers
Hint: This can only happen if x−2 is a factor of the numerator, so it can "cancel" the x−2 in the denominator. What does a have to be for this to be true?
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