what is the horizontal asymptote of the function $f(x)=\frac{(x - 2)}{(x - 3)^2}$?\no $y = 0$\no $y = 1$\no…

what is the horizontal asymptote of the function $f(x)=\frac{(x - 2)}{(x - 3)^2}$?\no $y = 0$\no $y = 1$\no $y = 2$\no $y = 3$

what is the horizontal asymptote of the function $f(x)=\frac{(x - 2)}{(x - 3)^2}$?\no $y = 0$\no $y = 1$\no $y = 2$\no $y = 3$

Answer

Explanation:

Step1: Determine degree of numerator and denominator

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

Step2: Apply horizontal - asymptote rule

When $n<m$, the horizontal asymptote of the rational function $y = \frac{f(x)}{g(x)}$ is $y = 0$. Here, since $1<2$, the horizontal asymptote of $f(x)=\frac{x - 2}{(x - 3)^2}$ is $y = 0$.

Answer:

A. $y = 0$