Respuesta :

the answer is a 
there's not a horizontal asymptote 
y = 0  

Answer:

A. [tex]y=0[/tex]

Step-by-step explanation:

We have been given a function [tex]f(x)=\frac{x-2}{(x-3)^2}[/tex] and we are asked to find the horizontal asymptote of our given function.

Let us recall the rules for a horizontal asymptote.

  • If polynomials of denominator and numerator of a rational function have same degree, then horizontal asymptote will be the quotient of coefficients of the highest degree terms.
  • If the polynomial of denominator has larger degree than the numerator, then the horizontal asymptote will be the x-axis or [tex]y=0[/tex].
  • If the polynomial of numerator has larger degree than denominator, then the function has no horizontal asymptote.

First of all let us expand the square given for the denominator.

[tex]f(x)=\frac{x-2}{x^2-6x+9}[/tex]

Now we can see that denominator of our triangle is a second degree polynomial, while numerator is a 1st degree polynomial.

Since denominator has larger degree than numerator, therefore, our function will have a horizontal asymptote at [tex]y=0[/tex] and option A is the correct choice.

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