Section: Calculus




Linear Functions

Non-linear Functions


Through language we are able to communicate with each other. The most common forms of language are: oral, written and graphical. Nowadays, graphics represent one way of expressing and transmitting information. The media often express information by means of tables and graphs as they offer a fast, visual interpretation as well as showing how certain variables depend on others.

Although most scientists in the XVII century were interested in the study of motion (e.g. paths of projectiles, distance travelled and greatest height reached; working out the position of a body out at sea and how to get to a place). The fact that measuring instruments lacked a high level of precision made it difficult to produce accurate tables for different variables and this prevented the study of functions happening earlier.

Newton (1642-1727) was first to deal with the concept of a function. he used the term "fluents" or "flowing quantities" to refer to any relationship between variables.

Leibniz (1646-1716) used the word "function" for the first time to refer to the quantities a variable depends on. He also used the words "constant, variable and parameter" for the first time in this context. Euler (1707-1783) is to thank for f(x), the form we commonly use now to express a function.

  • To become aware that a function is a concept which occurs naturally in many everyday situations.

  • To introduce concepts such as the rate of increase or convexity using the connection between verbal explanation and graphs.

  • To develop geometric intuition.

  • To awaken curiosity to discover relationships between different magnitudes.

  • To relate graphical language to other mathematical languages.

  Agustín Muñoz Núñez
© Spanish Ministry of Education. Year 2001

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