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The given function is \( r(x) = \frac{1}{x + 8} \), and it has a vertical asymptote at \( x = -8 \). 

Now, you are asked to find the equation of the vertical asymptote of \( r(-8x) \). 

### Step-by-Step Solution:

1. **Substitute \( -8x \) into the function \( r(x) \):**
   \[
   r(-8x) = \frac{1}{-8x + 8}
   \]
   
2. **Identify the vertical asymptote:**
   A vertical asymptote occurs when the denominator is equal to zero because the function becomes undefined. Therefore, solve for \( x \) when:
   \[
   -8x + 8 = 0
   \]
   
3. **Solve for \( x \):**
   \[
   -8x = -8
   \]
   \[
   x = 1
   \]

Thus, the vertical asymptote of \( r(-8x) \) is at \( x = 1 \).

### Final Answer:
The equation of the vertical asymptote is \( x = 1 \).

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Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. How do you find horizontal asymptotes of rational functions?
2. What changes when you scale the function vertically instead of horizontally?
3. What is the vertical asymptote of \( r(2x) \)?
4. How do transformations affect the location of asymptotes?
5. What is the general form of a rational function's asymptote equation?

**Tip:** Remember, vertical asymptotes occur when the denominator of a rational function equals zero, causing the function to become undefined.

Let r(x) = 1 / (x + 8). This function has a vertical asymptote at x = -8. What is the equation of the vertical asymptote of r(-8x)?

Learn how to find the vertical asymptote of the function r(-8x) based on the original function r(x) = 1 / (x + 8). This problem involves function transformations and determining asymptotes.

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