Question

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

$f(x)=\frac{4x + 1}{3x - 3}$

Explanation:

Step1: Find the denominator

The denominator of the function $f(x)=\frac{4x + 1}{3x - 3}$ is $3x-3$.

Step2: Set the denominator equal to zero

Set $3x - 3=0$.

Step3: Solve for $x$

$$\begin{align*} 3x-3&=0\\ 3x&=3\\ x& = 1 \end{align*}$$

Since the numerator $4x + 1$ when $x = 1$ is $4\times1+1=5
eq0$, so $x = 1$ is the vertical asymptote.

Answer:

$x = 1$