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To solve the inequality \( f(x) \geq 0 \) for the given graph, we need to identify where the function is non-negative (i.e., where it is either zero or positive).

### Analysis of the graph:
- The function appears to have an asymptote at \( x = 2 \), indicating that \( f(x) \) is undefined there.
- For \( x < 2 \), the graph is below the x-axis (negative), so \( f(x) < 0 \).
- For \( x = 2 \), the function does not exist, so it is not included in the solution.
- For \( x > 2 \), the function is above the x-axis (positive), meaning \( f(x) \geq 0 \) in this region.

### Interval notation solution:
The function \( f(x) \geq 0 \) for \( x > 2 \).

Thus, the solution in interval notation is:
\[
(2, \infty)
\]

Would you like more explanation about this solution?

Here are five related questions:
1. What does it mean when a function has a vertical asymptote?
2. How can you determine if a function is positive or negative just by looking at its graph?
3. What is interval notation, and why is it useful for inequalities?
4. How does the behavior of the function near asymptotes affect inequality solutions?
5. Can the inequality \( f(x) > 0 \) have different solutions than \( f(x) \geq 0 \)?

**Tip**: In interval notation, parentheses \( ( \) or \( ) \) exclude endpoints, while brackets \( [ \) or \( ] \) include them.

Solve the inequality f(x) ≥ 0 based on the given graph.

Learn how to solve the inequality f(x) ≥ 0 using interval notation based on a graph with a vertical asymptote at x = 2. Understand where the function is positive and the importance of asymptotic behavior in graph-based inequalities.

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