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To determine the intervals on which \( f(x) \geq 0 \) from the given graph, we need to identify the sections of the \( x \)-axis where the function \( f(x) \) is either positive (above the \( x \)-axis) or zero (on the \( x \)-axis).

Let's analyze the graph:

1. **Identify where \( f(x) = 0 \)**: These are the points where the graph crosses the \( x \)-axis.
2. **Locate intervals above the \( x \)-axis**: These are the intervals where the graph is positive, meaning \( f(x) > 0 \).

### Observing the Graph
From the graph, it appears that:
- \( f(x) = 0 \) at approximately \( x = -5 \), \( x = -3 \), \( x = 1 \), \( x = 4 \), and \( x = 7 \).
- The graph is above the \( x \)-axis (i.e., \( f(x) \geq 0 \)) on the following intervals:
  - \( x \in [-5, -3] \)
  - \( x \in [1, 4] \)
  - \( x \in [7, \infty) \)

### Final Answer
The intervals where \( f(x) \geq 0 \) are:
\[
[-5, -3] \cup [1, 4] \cup [7, \infty)
\]

Would you like further details on this solution or have any questions?

### Related Questions
1. How would the answer change if the question asked for \( f(x) > 0 \) instead of \( f(x) \geq 0 \)?
2. How do we determine where a function is decreasing or increasing on a graph?
3. What is the difference between intervals where \( f(x) \geq 0 \) and where \( f(x) > 0 \)?
4. How would we find the intervals where \( f(x) \leq 0 \) for this graph?
5. Can a polynomial function like this one have an infinite number of roots?

### Tip
Always check the points where the function touches or crosses the \( x \)-axis to determine intervals of non-negativity or non-positivity.

Determine all intervals on which f(x) ≥ 0.

Learn how to determine the intervals on which f(x) is greater than or equal to zero using graph analysis. Identify where the function is positive or zero by observing where it crosses the x-axis. This problem covers key mathematical concepts related to graph behavior and inequalities, suitable for students in Grades 10-12.

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