Question

find the vertical asymptote.
$y = \frac{3x + 27}{x - 9}$
$x = ?$

Explanation:

Step1: Recall vertical asymptote rule

For a rational function \( y = \frac{f(x)}{g(x)} \), vertical asymptotes occur where \( g(x) = 0 \) (and \( f(x)
eq 0 \) at those points, though here we first solve \( g(x)=0 \)).

Step2: Solve denominator \( x - 9 = 0 \)

Set the denominator equal to zero: \( x - 9 = 0 \). Solving for \( x \), we add 9 to both sides: \( x = 9 \).

Step3: Check numerator at \( x = 9 \)

Substitute \( x = 9 \) into the numerator \( 3x + 27 \): \( 3(9) + 27 = 27 + 27 = 54
eq 0 \). So the vertical asymptote is at \( x = 9 \).

Answer:

\( 9 \)