To find the vertical asymptote of the function [tex]\( y = \frac{3x + 12}{x - 6} \)[/tex], we need to determine where the denominator of the function equals zero, because at these points the function will be undefined, and typically, a vertical asymptote occurs.
Here are the step-by-step instructions to find the vertical asymptote:
1. Identify the denominator of the function:
The function given is [tex]\( y = \frac{3x + 12}{x - 6} \)[/tex]. The denominator is [tex]\( x - 6 \)[/tex].
2. Set the denominator equal to zero:
To find the vertical asymptote, set the denominator [tex]\( x - 6 \)[/tex] equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[
x - 6 = 0
\][/tex]
3. Solve the equation:
Solve for [tex]\( x \)[/tex]:
[tex]\[
x = 6
\][/tex]
Therefore, the vertical asymptote of the function [tex]\( y = \frac{3x + 12}{x - 6} \)[/tex] is at [tex]\( x = 6 \)[/tex].
