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?

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.