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To graph the function \( f(x) = -3 \log_2(-x) \), let's break down the requirements step-by-step:

1. **Understanding the Domain**:
   - Since \( \log_2(-x) \) only takes real values for \( -x > 0 \), we require \( x < 0 \). Thus, the function is defined for \( x < 0 \) only.

2. **Asymptote**:
   - As \( x \) approaches 0 from the left (i.e., \( x \to 0^- \)), \( -x \to 0^+ \) and \( \log_2(-x) \to -\infty \).
   - This causes \( f(x) \) to go to positive infinity. Hence, there is a vertical asymptote at \( x = 0 \).

3. **Selecting Points to Plot**:
   - Choose values of \( x \) that are negative, since \( f(x) \) is only defined for \( x < 0 \).
   - For example, try:
     - \( x = -1 \): \( f(-1) = -3 \log_2(1) = 0 \)
     - \( x = -2 \): \( f(-2) = -3 \log_2(2) = -3 \)
     - \( x = -4 \): \( f(-4) = -3 \log_2(4) = -6 \)
   - These points provide integer coordinates for easy plotting.

4. **Graph Characteristics**:
   - The graph should start near infinity on the left side of the \( y \)-axis and decrease as \( x \) becomes more negative.
   - The points \( (-1, 0) \), \( (-2, -3) \), and \( (-4, -6) \) are good reference points.

Would you like more details on the calculations, or have questions about any specific part?

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### Related Questions
1. What is the general behavior of logarithmic functions and their transformations?
2. How does the base of a logarithmic function affect its growth rate?
3. How does changing the sign in front of the logarithmic function affect its graph?
4. What is the effect of different vertical stretches/compressions on logarithmic graphs?
5. How do you determine asymptotes for logarithmic functions with transformations?

### Tip
For logarithmic functions, vertical transformations often alter the range without affecting the domain.

Graph the function f(x) = -3 log_2(-x) on the axes below. You must plot the asymptote and any two points with integer coordinates.

This guide explains how to graph the function f(x) = -3 log_2(-x), including finding the vertical asymptote and plotting integer-coordinate points. Learn about the domain restrictions, asymptotic behavior, and transformations for logarithmic functions.

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