To find the vertical asymptote of the function [tex]\( y = \frac{3x - 6}{x + 2} \)[/tex], we need to determine where the function is undefined. A function is undefined where its denominator is equal to zero because division by zero is undefined in mathematics.
Let's identify the value of [tex]\( x \)[/tex] that makes the denominator zero:
1. Start with the denominator of the function:
[tex]\[
x + 2
\][/tex]
2. Set the denominator equal to zero to find the value of [tex]\( x \)[/tex]:
[tex]\[
x + 2 = 0
\][/tex]
3. Solve the equation for [tex]\( x \)[/tex] by isolating [tex]\( x \)[/tex]:
[tex]\[
x = -2
\][/tex]
Therefore, the function [tex]\( y = \frac{3x - 6}{x + 2} \)[/tex] is undefined at [tex]\( x = -2 \)[/tex].
As a result, the vertical asymptote of the function occurs at:
[tex]\[
x = -2
\][/tex]
Thus, the vertical asymptote is [tex]\( x = -2 \)[/tex].
