find the equation of all vertical asymptotes of the following function.\n\n$f(x)=\\frac{4x + 1}{3x - 3}$

Answer:

$x = 1$

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 $4\times1+1=5\neq0$, so $x = 1$ is the vertical asymptote.