What is the horizontal asymptote of the function f(x)=(x-2)/(x-3)^2

Question

What is the horizontal asymptote of the function f(x)=(x-2)/(x-3)^2

in progress 0
2022-05-24T15:25:18+00:00 2 Answers 0

Answers ( 2 )

  1. Aaliyah
    0
    2022-05-24T15:26:48+00:00

    Answer:

    The horizontal asymptote of the function is y=0.

    Step-by-step explanation:

    Given : [tex]f(x)=frac{(x-2)}{(x-3)^2}[/tex]

    To find : What is the horizontal asymptote of the function?

    Solution :

    In a rational function,

    If the degree of the numerator < degree of denominator then a horizontal asymptote can be found.n

    In the given function,

    [tex]f(x)=frac{(x-2)}{(x-3)^2}[/tex]

    The degree of numerator is 1.

    The degree of denominator is 2

    The degree of the numerator < degree of denominator

    nWhen this condition satisfy then horizontal asymptote is always y=0

    Therefore, The horizontal asymptote of the function is y=0.

  2. Eden97
    0
    2022-05-24T15:27:15+00:00

    To find this, take the limit of the given function as x increases without bound. Because the highest x power in the numerator (1) is smaller than that in the denominator, f(x) tends to zero as x increases without bound. Thus, the equation of the horiz. asy. here is y = 0.

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