Question

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

Answer 1

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.

Answer 2

Answer:

The horizontal asymptote of the function is y=0.

Step-by-step explanation:

Given : $f(x)=\frac{(x-2)}{(x-3)^2}$

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.

In the given function,

$f(x)=\frac{(x-2)}{(x-3)^2}$

The degree of numerator is 1.

The degree of denominator is 2

The degree of the numerator < degree of denominator

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

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