what is the horizontal asymptote of the function $f(x)=\frac{(x - 2)}{(x - 3)^2}$?\n$y = 0$\n$y = 1$\n$y =…

what is the horizontal asymptote of the function $f(x)=\frac{(x - 2)}{(x - 3)^2}$?\n$y = 0$\n$y = 1$\n$y = 2$\n$y = 3$

what is the horizontal asymptote of the function $f(x)=\frac{(x - 2)}{(x - 3)^2}$?\n$y = 0$\n$y = 1$\n$y = 2$\n$y = 3$

Answer

Explanation:

Step1: Determine degree of numerator and denominator

The degree of the numerator of $f(x)=\frac{x - 2}{(x - 3)^2}=\frac{x - 2}{x^{2}-6x + 9}$ is $n = 1$ (highest - power of $x$ in numerator) and the degree of the denominator is $m=2$ (highest - power of $x$ in denominator).

Step2: Apply horizontal - asymptote rule

When $n<m$ (where $n$ is the degree of the numerator and $m$ is the degree of the denominator of a rational function $y=\frac{f(x)}{g(x)}$), the horizontal asymptote is $y = 0$.

Answer:

A. $y = 0$