An odd function is a mathematical function where the output value changes sign when the input value is changed to its opposite value. This means that if the input is multiplied by -1, the output will also be multiplied by -1. This property is also known as rotational symmetry.
An even function is a mathematical function where the output value remains the same when the input value is changed to its opposite value. This means that if the input is multiplied by -1, the output will remain unchanged. This property is also known as reflectional symmetry.
To determine if a function is odd or even, you can use the symmetry tests. For an odd function, plug in -x for x and if the resulting output is the negative of the original output, then the function is odd. For an even function, plug in -x for x and if the resulting output is the same as the original output, then the function is even.
Some examples of odd functions include polynomial functions with odd exponents, such as f(x) = x^3, and trigonometric functions like sine and tangent.
No, a function cannot be both odd and even. This is because the properties of odd and even functions are mutually exclusive. If a function is odd, it cannot have reflectional symmetry and if a function is even, it cannot have rotational symmetry.