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Let's analyze each graph to determine where \( f(x) \leq 0 \) and express it using interval notation.

### Part (a)
For graph (a), \( f(x) \) is less than or equal to zero in the following intervals:
1. The graph crosses or touches the x-axis around \( x = -4 \) and \( x = -2 \), and is below the x-axis between these points.
2. Similarly, it crosses around \( x = 0 \) and \( x = 2 \), and is below the x-axis between these points.

Thus, in interval notation, where \( f(x) \leq 0 \) for part (a) is:
\[
(-4, -2) \cup (0, 2)
\]

### Part (b)
For graph (b), \( f(x) \leq 0 \) in the following intervals:
1. The function crosses or touches the x-axis around \( x = -3 \) and \( x = 1 \). It is below or equal to the x-axis between these points.

So, in interval notation, where \( f(x) \leq 0 \) for part (b) is:
\[
[-3, 1]
\]

### Final Answer in Set Notation
- **(a)** \( x \in (-4, -2) \cup (0, 2) \)
- **(b)** \( x \in [-3, 1] \)

Would you like more details on any of these steps?

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Here are five related questions to extend your understanding:
1. How do you determine where a function is positive or negative from a graph?
2. What does it mean for a graph to be symmetric with respect to the y-axis?
3. How can interval notation be used to describe the range of a function?
4. What are the different types of intervals (open, closed, half-open) and when do you use each?
5. How can you find the points of intersection between a function and the x-axis?

**Tip:** When reading a graph, remember that a function is zero at the x-intercepts, positive above the x-axis, and negative below the x-axis.

For each graph shown, determine where f(x) ≤ 0. Express your answers using interval notation.

Learn how to analyze graphs to find where f(x) ≤ 0 and express answers using interval notation. This solution includes step-by-step reasoning for each graph, helping students understand inequalities and interval notation. Ideal for Grades 9-12.

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