To find the vertical asymptote of the given function:

$y = \frac{3x - 9}{x - 5}$

Step 1: Identify the Denominator

Vertical asymptotes occur where the denominator is equal to zero, provided that the numerator does not also become zero at the same point.

Set the denominator equal to zero:

$x - 5 = 0$

$x = 5$

Step 2: Verify if It’s a True Asymptote

Since the numerator $3x - 9$ does not become zero when $x = 5$, there is no hole in the graph. This confirms that $x = 5$ is a vertical asymptote.

Final Answer:

The vertical asymptote is $x = 5$.

Would you like a graph or further explanation?

Related Questions:

1. How do you find horizontal asymptotes for rational functions?
2. What happens if both the numerator and denominator have a common factor?
3. How do you determine slant asymptotes?
4. Can a rational function have multiple vertical asymptotes?
5. How does the degree of the numerator and denominator affect asymptotes?

Math Tip:

For rational functions, vertical asymptotes occur at values that make the denominator zero, as long as they don’t cancel with the numerator.