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The problem asks to determine the intervals on which \( f(x) \geq 0 \) based on the given graph.

### Analyzing the graph:
We can see the behavior of the function, and we need to focus on the intervals where the function \( f(x) \) is either positive or zero. From visual inspection, the function crosses the x-axis at certain points, and between those points, the function will be either positive or negative.

### Steps:
1. **Identify the x-intercepts (where \( f(x) = 0 \))**: These are points where the curve touches or crosses the x-axis.
2. **Determine the intervals where \( f(x) > 0 \)**: Look at the segments of the curve that lie above the x-axis.
3. **Include the x-intercepts as part of the solution**: Since the function is required to be non-negative (\( f(x) \geq 0 \)), the x-intercepts should be included in the intervals.

### X-Intercepts from the graph:
The graph crosses the x-axis at approximately \( x = -3 \), \( x = 0 \), and \( x = 5 \).

### Intervals where \( f(x) \geq 0 \):
- From \( x = -3 \) to \( x = 0 \), the function is positive.
- From \( x = 5 \) onward, the function is positive again.

### Conclusion:
The intervals where \( f(x) \geq 0 \) are:
\[
[-3, 0] \cup [5, \infty)
\]

Would you like further details or have any questions?

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Here are 5 follow-up questions that relate to this topic:
1. How do you find the roots of a function algebraically from its equation?
2. What is the difference between \( f(x) > 0 \) and \( f(x) \geq 0 \) in terms of intervals?
3. How can you determine if a function is increasing or decreasing based on its graph?
4. What are the conditions for a function to be continuous on a given interval?
5. How do we calculate the derivative of a function from its graph?

**Tip**: Always include endpoints in your intervals when the problem asks for non-negative values (i.e., \( \geq 0 \)), since zeros are included in the solution.

Determine all intervals on which f(x) ≥ 0 based on the given graph.

Determine the intervals where the function f(x) is greater than or equal to 0 using the graph. Learn how to analyze x-intercepts and understand the behavior of the function on specific intervals. Ideal for students in Grades 9-12.

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