To find the vertical asymptote of the function:

$y = \frac{4x + 32}{x - 8}$

Step 1: Identify the Denominator

Vertical asymptotes occur where the denominator is zero (since division by zero is undefined).

The denominator of the given function is:

$x - 8$

Step 2: Solve for $x$

Set the denominator equal to zero:

$x - 8 = 0$

$x = 8$

Conclusion:

The vertical asymptote is at:

$x = 8$

Would you like a further explanation or any additional details?

Related Questions:

1. How do you determine horizontal asymptotes for rational functions?
2. What is the domain of the given function?
3. How do you find the x-intercepts of a rational function?
4. What happens to the function as $x$ approaches the vertical asymptote?
5. How do you determine if there is a hole in the function?

Tip:

Always check for common factors in the numerator and denominator, as they might cancel out, leading to holes in the graph instead of asymptotes.