Question

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

Answer 1

Answer:

A. $y=0$

Step-by-step explanation:

We have been given a function $f(x)=\frac{x-2}{(x-3)^2}$ 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 $y=0$.
• 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.

$f(x)=\frac{x-2}{x^2-6x+9}$

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 $y=0$ and option A is the correct choice.

Answer 2

The answer is a 
there's not a horizontal asymptote 
y = 0  <span />