To determine the vertical asymptote of the function [tex]\( y = \frac{8x + 8}{x - 4} \)[/tex], we need to consider where the function is undefined. A vertical asymptote occurs where the denominator of the function is equal to zero, as division by zero is undefined.
Here are the steps to find the vertical asymptote:
1. Identify the denominator of the function which is [tex]\( x - 4 \)[/tex].
2. Set the denominator equal to zero to find the value(s) of [tex]\( x \)[/tex] where the function is undefined:
[tex]\[
x - 4 = 0
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = 4
\][/tex]
Therefore, the vertical asymptote of the function [tex]\( y = \frac{8x + 8}{x - 4} \)[/tex] occurs at [tex]\( x = 4 \)[/tex].
So, the vertical asymptote is [tex]\( x = 4 \)[/tex].
