An odd function is a mathematical function where the output or value of the function for a negative input is the opposite of the output for the corresponding positive input. In other words, an odd function is symmetric about the origin.
A function can be determined to be odd if it follows the rule f(-x) = -f(x), where f(x) is the function and -x is the negative input. This means that plugging in a negative input will result in the opposite output of the positive input.
The graph of an odd function will be symmetric about the origin, meaning that it will have rotational symmetry of 180 degrees. It will also pass through the origin, where the input and output values are both 0.
Yes, an odd function can have both positive and negative outputs. This is because the function's output will be the opposite of the input, not necessarily always positive or always negative.
Some common real-life examples of odd functions include the sine and tangent functions, which describe the relationship between the angles of a triangle. Other examples include the velocity of an object in simple harmonic motion or the displacement of a pendulum.