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Inverse functions

tipo de documento Mathematics - Teaching sequence

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Inverse functions

Worksheet overview

Description:

The origin of the concept of functions has always been closely linked to the study of the phenomena of change. The oldest written references can be found amongst the writings of Babylonian astronomers. In the Middle Ages the study of functions appeared to be linked to the concept of movement. Nicole Oresme (1323-1392), a scholar interested in this concept, gave graphical representations showing change in velocity with respect to time. Three centuries later, Galileo studied movement from a quantitative point of view, justified his discoveries experimentally and established laws between different magnitudes. After Galileo, the concept of the function evolved until, in the XIXth century, in 1837, Dirichlet defined the function as a relation between variables, which is the definition we still use today. Functions are a basic tool which are used in physics, biology, social sciences and so on.

Teaching orientation:

KNOWLEDGE TYPE: declarative, procedural

PRIOR KNOWLEDGEThe contents required are explained in this course

LEARNING OBJECTIVESRecognise a function graphically Find the domain and range of a function both graphically and analytically Use the graph of a function to see if it has an inverse. Find the inverse of a few simple functions using analytical methods. Use a graph to find the table of values of an inverse function for more complex functions.

License:
creative commons: attribution - non commercial - share alike
License description:

The use of the following contents is universal, free of charge and open, provided that it is for noncommercial educative use. The actions, products and utilities derived from its use are therefore not allowed to generate any profit. Moreover, a reference to the source is required.

End user:
learner
Context:
schoolmate

General

Language:
english
KeyWords: inverse functions definition of a function domain of a function range of a function
Scope: universal
Structure:
linear
Agregation level:
Teaching Sequence
Collection: Descartes
Node:
Repository URL: /repositorio/20072010/9d/es_2010072063_9174709
IMS Manifest Download file

Technique

Format:
image/gif
text/html
Requirement type:
operating system
Requirement name:
multi-os
Requirement type:
browser
Requirement name:
any
Installation considerations:

Installation is not required

Other platform requirements:

Install and enable the Java interpreter and Plug-in of the applet Descartes on local

Educational use

Educational learning resource type:
real or virtual learning environment
Interaction type:
mixed
Interaction level:
low
Semantic density:
medium
Age: 16
Difficulty:
medium
Learning time: 2 teaching units
Educational language:
english
Cognitive process:
practise
understand
prove

Rights

License cost:
no
Access type:
universal
Access description:

es_cnice_20080623,es_{nodo}_20080923,es_clm_20091103121523455,es_murcia_20080422121523455,es_valencia_20081215,es_contenidos_20080623,es_castillayleon_201002241811,es_baleares_200907131205,es_canarias_20090114,es_aragon_20080930,es_larioja_20081107,es_cantabria_20081215,es_euskadi_20100423,es_extremadura_20090126,es_navarra_20090202,es_andalucia_20090324

Conceptual map: Inverse functions

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Fecha publicación: 28.3.2015

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