Question 4 (2 marks)
The following facts are known for the function $y=f(x)$.
- The function is continuous for all values of $x$.
- The function is neither even nor odd.
- The function is negative between $x=-2$ and $x=0$ and between $x=2$ and $x=4$.
The graph of $y=|f(|x|)|$ is given below. Sketch two possible graphs of $y=f(x)$.
1

Step 1 ：Since the function is neither even nor odd, we cannot use the properties of even or odd functions to determine the behavior of the graph.

Step 2 ：We know that the function is negative between $x=-2$ and $x=0$ and between $x=2$ and $x=4$. We also know that the graph of $y=|f(|x|)|$ is given.

Step 3 ：To sketch two possible graphs of $y=f(x)$, we can use the information from the graph of $y=|f(|x|)|$ and the given facts about the function.

Step 4 ：For the first possible graph, we can reflect the graph of $y=|f(|x|)|$ over the y-axis and then reflect the negative portions over the x-axis. This will give us a graph that is negative between $x=-2$ and $x=0$ and between $x=2$ and $x=4$.

Step 5 ：For the second possible graph, we can modify the first graph by adding some wiggles or bumps in the positive regions, as long as the function remains continuous and satisfies the given conditions.

Step 6 ：\(\boxed{\text{Two possible graphs of } y=f(x) \text{ have been sketched.}}\)