How to Determine if a Graph is Even or Odd

To determine if a graph is even or odd, you need to analyze the function that defines the graph.

A graph is considered even if it satisfies the condition:

• f(x) = f(-x)

This means that for every point (x, f(x)) on the graph, there is a corresponding point (-x, f(-x)) at the same height, which creates symmetry about the y-axis.

On the other hand, a graph is odd if it satisfies the condition:

• f(x) = -f(-x)

This indicates that for every point (x, f(x)), there is a corresponding point (-x, -f(-x)), resulting in symmetry about the origin.

To check if a graph is even or odd:

1. Substitute a value of x into the function and find f(x).
2. Then substitute -x into the function to find f(-x).
3. Compare the results:
• If f(x) equals f(-x) for all x, the graph is even.
• If f(x) equals -f(-x) for all x, the graph is odd.
• If neither condition holds true, the graph is neither even nor odd.

Visualizing the graph can also help; even functions appear symmetric about the y-axis, while odd functions are symmetric about the origin.