To determine if a function is even, odd, or neither using its graph, we can use the following criteria:
- A function is even if it is symmetric about the y-axis. This means that for every point (x, y) on the graph, the point (-x, y) is also on the graph.
- A function is odd if it is symmetric about the origin. This means that for every point (x, y) on the graph, the point (-x, -y) is also on the graph.
- If the graph does not exhibit either of these symmetries, then the function is considered neither.
To analyze the graph, look for points where both (x, y) and (-x, y) exist to check for evenness, and where both (x, y) and (-x, -y) exist to check for oddness. If neither condition holds for all points on the graph, the function fits the ‘neither’ category.
In summary, closely examine the graph for symmetry. This will help you categorize the function accurately. If you find it symmetric about the y-axis, it is even; if symmetric about the origin, it is odd; otherwise, it is neither.