Question

find the equation of all vertical asymptotes of the following function.

$f(x)=\frac{2x - 6}{6x + 12}$

answer: y =

Explanation:

Step1: Find the denominator

The denominator of the function \(f(x)=\frac{2x - 6}{6x + 12}\) is \(6x+12\).

Step2: Set the denominator equal to zero

Set \(6x + 12=0\).

Step3: Solve the equation

Subtract \(12\) from both sides: \(6x=-12\).
Divide both sides by \(6\): \(x=\frac{-12}{6}=-2\).
Since the numerator \(2x - 6\) at \(x = - 2\) is \(2\times(-2)-6=-4 - 6=-10
eq0\), \(x=-2\) is the vertical asymptote.

Answer:

$x = - 2$