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?

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.