Explain the word transformation and how it differs from the word translation. give an example.

A transformation refers to a way in which a function is modified such that the resulting curve differs in some geometric way. For example, scaling and translating are both transformations. Mathematically, a transformation can be described as two functions and such that for some function , a transformed version of is any function

A translation specifically refers to some real numbers h and k such that given a linear function , a translation of is any function . More generally, a translation is a type of transformation where and .

Consider the function . A translation is any function of the form . Now consider how a transformation differs from a translation in terms of scaling , where and such that a transformed version of is some function . For all values of h and k,

yes. we do proportions in probabilities.