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The question asks which graph represents the function \( y = \log_2 x \).

Key characteristics of the logarithmic function \( y = \log_2 x \):

1. **Domain**: The function is only defined for \( x > 0 \), so the graph must be entirely to the right of the y-axis.
2. **Vertical asymptote**: There is a vertical asymptote at \( x = 0 \), meaning the curve approaches but never touches or crosses the y-axis.
3. **Shape**: The logarithmic graph increases slowly for larger values of \( x \) but rapidly decreases near 0 on the positive x-axis.
4. **Intercept**: The graph will pass through \( (1, 0) \) because \( \log_2(1) = 0 \).

Looking at the four graphs:

- **Top left**: This graph is defined for negative x-values and approaches the x-axis from the left, which doesn't match a logarithmic function.
- **Top right**: This is an exponential curve, not a logarithmic curve.
- **Bottom left**: This is also incorrect as it represents a negative logarithmic-like shape.
- **Bottom right**: This graph fits the description of \( y = \log_2 x \), defined only for \( x > 0 \), with a vertical asymptote at \( x = 0 \), and passing through \( (1, 0) \).

Thus, the correct graph is the **bottom right** one.

Would you like more details or have any questions?

Here are five related questions to explore:

1. How does the base of a logarithm affect the shape of its graph?
2. What is the inverse of the function \( y = \log_2 x \)?
3. Can you explain the domain and range of logarithmic functions?
4. How would the graph of \( y = \log_3 x \) compare to \( y = \log_2 x \)?
5. What happens to the graph of \( y = \log_2 x \) if you add a constant to the function (e.g., \( y = \log_2 x + 2 \))?

**Tip**: When sketching logarithmic graphs, always check for the vertical asymptote at \( x = 0 \) and where the function crosses the x-axis (at \( (1, 0) \)).

In this exercise, students are asked to identify the graph representing the function y = log2 x. The problem requires an understanding of logarithmic functions, their domain, asymptotes, and general shape. The graph has a vertical asymptote at x = 0 and passes through (1, 0). Suitable for students in Grades 10-12.

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