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The notion of a function is the mathematical way of formalising the idea that one or more independent quantities are assigned to one or more dependent quantities. Functions in general and their investigation are at the core of analysis. They help to model dependencies of variable quantities, from simple planar graphs, curves and surfaces in space to solutions of differential equations or the algorithmic construction of fractals. One the one hand, this chapter serves to introduce the basic concepts. On the other hand, the most important examples of real-valued, elementary functions are discussed in an informal way. These include the power functions, the exponential functions and their inverses. Trigonometric functions will be discussed in Chap. 3, complex-valued functions in Chap. 4.