After the change of variables, a posynomial becomes a sum of exponentials of affine functions.

It is a piecewise-defined function whose pieces are affine functions.

Linear functions may be confused with affine functions.

One variable affine functions can be written as .

Although affine functions make lines when graphed, they do not satisfy the properties of linearity.

In that information environment, admissible transformations are increasing affine functions and, in addition, the scaling factor must be the same for everyone.

In mathematical language, the price is an affine function (sometimes also linear function) of the quantity bought.

Hence, if b 0, the function is often called an affine function (see in greater generality affine transformation).

Linearity constraint qualification: If and are affine functions, then no other condition is needed.

The diagram shows the construction on an IFS from two affine functions.