non-linear functions

A non-linear function is one that includes elements that cannot be expressed as a simple linear multiples of variables. For example, x², 2ⁿ, exp(x) and log(x+y) are all non-linear functions. Note that a non-linear function may include parts that are linear so long as there are some parts that cannot be reduced to a linear sum; for example the classic quadratic ax²+bx+c is a non linear function of x. Note that non-linear functions may include discontinuities, such as the hardthreshold step function, or complete changes in form. As linear functions are easier to deal with, it may sometimes be useful to use a piecewise linear approximation ti a non linear function.