Question

find the horizontal asymptote.
$y = \frac{4x + 12}{4x - 12}$
$y = ?$

Explanation:

Step1: Divide numerator and denominator by \(x\)

$$y=\frac{\frac{4x}{x}+\frac{12}{x}}{\frac{4x}{x}-\frac{12}{x}}=\frac{4 + \frac{12}{x}}{4-\frac{12}{x}}$$

Step2: Find the limit as \(x\to\pm\infty\)

As \(x\to\pm\infty\), \(\frac{12}{x}\to0\). So \(y=\lim_{x\to\pm\infty}\frac{4 + \frac{12}{x}}{4-\frac{12}{x}}=\frac{4 + 0}{4-0}\)

Answer:

\(y = 1\)