## 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

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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. 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.