Question

find the horizontal asymptote.
y = \frac{6x - 24}{2x + 12}
y = ?

Explanation:

Step1: Analyze degrees of numerator and denominator

The given function is \( y = \frac{6x - 24}{2x + 12} \). The degree of the numerator (highest power of \( x \)) is 1, and the degree of the denominator is also 1. When the degrees of the numerator and denominator are equal, the horizontal asymptote is the ratio of the leading coefficients.

Step2: Find leading coefficients

The leading coefficient of the numerator \( 6x - 24 \) is 6, and the leading coefficient of the denominator \( 2x + 12 \) is 2.

Step3: Calculate the ratio

The ratio of the leading coefficients is \( \frac{6}{2}=3 \). So the horizontal asymptote is \( y = 3 \).

Answer:

\( y = 3 \)