Question

find the value of x where the given function has a vertical asymptote.
f(x) = \frac{1}{x - 3}
x = ?

Explanation:

Step1: Recall vertical - asymptote condition

A rational function $y = \frac{f(x)}{g(x)}$ has a vertical asymptote at $x = a$ when $g(a)=0$ and $f(a)
eq0$. For the function $f(x)=\frac{1}{x - 3}$, we set the denominator equal to zero.
$x-3 = 0$

Step2: Solve for x

Add 3 to both sides of the equation $x-3 = 0$.
$x=3$

Answer:

$x = 3$