find the horizontal asymptote.\nhint: what is the ratio of the leading coefficients?\n$y = \\frac{3x - 6}{x…

Answer:

$y = 3$

Explanation:

Step1: Identify the degrees of numerator and denominator

The degree of the numerator $3x - 6$ is 1 and the degree of the denominator $x + 2$ is 1.

Step2: Find the horizontal - asymptote formula

When the degrees of the numerator and denominator of a rational function $\frac{f(x)}{g(x)}$ are the same (both $n$), the horizontal asymptote is given by $y=\frac{a_n}{b_n}$, where $a_n$ and $b_n$ are the leading coefficients of $f(x)$ and $g(x)$ respectively.

Step3: Determine the leading coefficients

The leading coefficient of the numerator $3x - 6$ is $a_n = 3$, and the leading coefficient of the denominator $x + 2$ is $b_n=1$.

Step4: Calculate the horizontal asymptote

$y=\frac{3}{1}=3$.