Questions: Even Odd Neither

Solution Steps

To determine if the function is even, odd, or neither, we need to analyze its symmetry.

• A function \( f(x) \) is even if \( f(-x) = f(x) \) for all \( x \) in the domain.
• A function \( f(x) \) is odd if \( f(-x) = -f(x) \) for all \( x \) in the domain.
• If neither condition is met, the function is neither.

Examine the graph to see if it exhibits symmetry:

• Even Function: Symmetric about the y-axis.
• Odd Function: Symmetric about the origin.

From the graph, observe the following:

• The function does not exhibit symmetry about the y-axis.
• The function does exhibit symmetry about the origin. If you rotate the graph 180 degrees around the origin, it looks the same.

Final Answer