To determine if a function is even or odd by examining its graph, we look at its symmetry:

1. Even function: A function is even if it is symmetric with respect to the y-axis. This means that if we reflect the graph across the y-axis, it would appear unchanged. Mathematically, an even function satisfies $f(x) = f(-x)$ for all $x$ in the domain.

2. Odd function: A function is odd if it is symmetric with respect to the origin. This means that if we rotate the graph 180 degrees around the origin, it would appear unchanged. Mathematically, an odd function satisfies $f(-x) = -f(x)$ for all $x$ in the domain.

From the description, the graph crosses the x-axis symmetrically at $x = -2$ and $x = 2$, with a similar pattern of minima and maxima on either side of the y-axis. This pattern indicates symmetry with respect to the origin (since it mirrors across both the x and y axes).

Thus, the function is odd because it is symmetric with respect to the origin.

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Would you like further clarification on symmetry in functions? Here are some related questions you may find helpful:

1. What is the general test to determine if a function is even or odd based on its equation?
2. Can a function be both even and odd?
3. How can we identify even and odd functions if the graph is less symmetrical?
4. How do transformations affect the evenness or oddness of a function?
5. Are all polynomial functions even or odd?

Tip: When analyzing functions visually, symmetry across the y-axis suggests an even function, while symmetry about the origin suggests an odd function.