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Show all work to identify the asymptotes and state the end behavior of the function f(x) = 6x/ x - 36

Show all work to identify the asymptotes and state the end behavior of the function-example-1

1 Answer

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Vertical asymptotes are when the denominator is 0 but the numerator isn't 0.


x-36=0 \implies x=36

Since this value of x does not make the numerator equal to 0, the vertical asymptote is
x=36.

Horizontal asymptotes are the limits as
x \to \pm \infty.


\lim_(x \to \infty) (6x)/(x-36)=\lim_(x \to \infty)=(6)/(1-(36)/(x))=6\\\\\lim_(x \to -\infty) (6x)/(x-36)=\lim_(x \to -\infty)=(6)/(1-(36)/(x))=6\\\\

So, the horizontal asymptote is
y=6.

End behavior:

  • As
    x \to \infty, f(x) \to -\infty
  • As
    x \to -\infty, f(x) \to \infty.
User Muhammad Suleman
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