Graph $\"f\"$ :

A function is odd function if the graph of the function is symmetric about the origin.

Observe the graph.

The graph $\"f\"$ is odd function, because it is symmetric about the origin.

Graph $\"g\"$ :

A function is even function if the graph of the function is symmetric about the $\"y-\"$ axis.

Observe the graph.

The graph $\"g\"$ is even function, because it is symmetric about the $\"y-\"$ axis.

The function on one side of the graph $\"g\"$ is reflects on other side.

$\"f\"$ is odd function.

$\"g\"$ is even function.