# Changes

## Function

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A '''function ''' f is a rule for taking one item x, as an input, and producing another item f(x) as an output. Frequently this will involve numbers, so for example the [[polynomial]] f(x) = x^2 takes numbers as inputs, and outputs their squares. So in this case, if 1 is input, 1 is output, whilst if 2 is input, 4 is output. However, there are functions that take other objects as inputs. For example, rotation can be thought of as a function that takes a shape as an input, and outputs that shape rotated by a certain number of degrees.

Usually, a function will be written with a formula for the output, in terms of the input. For example, in the case of f above, the formula is f(x) = x^2. When we want to input a particular value, we insert in in the place of x. So f(1) = 1^2 = 1*1 = 1.