Asymptotes of functionHow 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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Asymptotes of functionHow to find a if the function below doesn&#039;t have a vertical asymptotes.  f  (  x  )  =                    x        2            −      a      x      +      2              x      −      2

penangrl · Accepted Answer

A function like that has vertical asymptote when it&#039;s denominator is 0, that happens when x=2  f  (  x  )  =                    x        2            −      a      x      +      2              x      −      2      But since we don&#039;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  )

Haley Madden · Accepted Answer

Hint: This can only happen if x−2 is a factor of the numerator, so it can &quot;cancel&quot; the x−2 in the denominator. What does   a have to be for this to be true?

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

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