Question

find the horizontal asymptote.
$y = \frac{6x - 12}{2x + 12}$
$y = ?$

Explanation:

Step1: Recall Horizontal Asymptote Rule

For a rational function \( y = \frac{f(x)}{g(x)} \) where \( f(x) \) and \( g(x) \) are polynomials, if the degrees of \( f(x) \) and \( g(x) \) are equal, the horizontal asymptote is \( y=\frac{\text{leading coefficient of } f(x)}{\text{leading coefficient of } g(x)} \).

Step2: Identify Degrees and Coefficients

In \( y = \frac{6x - 12}{2x + 12} \), the degree of numerator \( 6x - 12 \) is 1, and the degree of denominator \( 2x + 12 \) is also 1 (equal degrees). The leading coefficient of numerator is 6, and of denominator is 2.

Step3: Calculate Horizontal Asymptote

Using the rule, \( y=\frac{6}{2}=3 \).

Answer:

\( y = 3 \)