To find the vertical asymptote of the rational function [tex]\( y = \frac{6x - 18}{x + 9} \)[/tex], we need to determine the values of [tex]\( x \)[/tex] for which the denominator is zero, as these values make the function undefined and create vertical asymptotes.
Here are the steps to find the vertical asymptote:
1. Identify the Denominator:
The denominator of the given function is [tex]\( x + 9 \)[/tex].
2. Set the Denominator Equal to Zero:
To find the vertical asymptote, we set the denominator equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[
x + 9 = 0
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Solving the equation above, we get:
[tex]\[
x = -9
\][/tex]
Therefore, the vertical asymptote of the function [tex]\( y = \frac{6x - 18}{x + 9} \)[/tex] occurs at:
[tex]\[
x = -9
\][/tex]
This means that as [tex]\( x \)[/tex] approaches [tex]\(-9\)[/tex], the value of the function [tex]\( y \)[/tex] tends towards positive or negative infinity.
