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The given function is:

\[
r(x) = \frac{1}{x + 8}
\]

It is stated that this function has a vertical asymptote at \( x = -8 \), which occurs because the denominator \( x + 8 = 0 \) at \( x = -8 \).

Now, the problem asks for the equation of the vertical asymptote of the transformed function \( r(-8x) \).

### Step-by-Step Analysis

The new function \( r(-8x) \) can be written as:

\[
r(-8x) = \frac{1}{-8x + 8}
\]

We need to find the value of \( x \) that makes the denominator zero, which will give us the vertical asymptote. So, set the denominator equal to zero:

\[
-8x + 8 = 0
\]

Solve for \( x \):

\[
-8x = -8
\]

\[
x = 1
\]

### Conclusion
The equation of the vertical asymptote of the transformed function \( r(-8x) \) is:

\[
x = 1
\]

Would you like further details or clarification on any step?

### Related Questions:
1. How do you find horizontal asymptotes for rational functions?
2. What happens to the asymptotes when a function is reflected over the y-axis?
3. Can a function have more than one vertical asymptote?
4. What is the effect of multiplying the input of a function by a constant on its graph?
5. How do horizontal shifts affect the position of asymptotes?

### Tip:
Always check how transformations such as reflections or stretches/compressions affect both the location of the asymptotes and the overall shape of the graph.

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 a transformed function r(-8x), starting from r(x) = 1/(x + 8). The solution involves understanding how transformations affect asymptotes in rational functions. Suitable for students in Grades 9-12.

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