# Real Functions

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## Functions in real life

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### Table of Contents

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Explore subjects Browse subject categories to explore new topics or look for reference material for a course you are already studying. Some functions like Reduce , FindInstance , etc. ComplexExpand[] and sometimes FunctionExpand[] may also be useful in similar situations but not really here. Generally , as far as I know, there is no mathematical way to tell Mathematica that a variable is real. It is only possible to do this in a formal way, using patterns, and only for certain functions that have the Assumptions option. By "formal" I mean that if you tell it that a[x] is real, it will not know automatically that a'[x] is also real.

Note that doing something like ComplexExpand[Norm[a'[s], 2]] or indeed ComplexExpand[Norm[a'[s], p]] where p is a rational number doesn't work for some reason. For older Mathematica versions there used to be an add-on package RealOnly that put Mathematica in a reals-only mode. There is a version available in later versions and online with minimal compatibility upgrades. It reduces many situations to a real-only solution, but doesn't work for your Norm case:.

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## Introduction to real functions

Working with real functions in mathematica Ask Question. Asked 7 years, 9 months ago. Active 7 years, 9 months ago. Viewed 6k times. Knowledge of the symmetries of the graphs of odd and even functions is useful in curve sketching. Its graph is symmetric with respect to reflection in the y-axis, i. Its graph is symmetric with respect to reflection in the point 0 the origin or axes , i. Some of the work of this section might profitably be discussed in conjunction with Topics 6 and 9.

A circle with a given centre C and a given radius r is defined as the set of points in the plane whose distance from C is r. Generally, sets of points satisfying simple conditions stated in geometrical terms can be described in algebraic terms by introducing cartesian coordinates and interpreting the original conditions as conditions relating x and y. The conditions then usually reduce to one or more equations or inequalities.

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## Continuity for Real functions

Treatment is to be restricted to regions of the cartesian x, y— plane which admit a simple geometrical description — for example, by use of words such as interior, exterior, bounded by, boundary, sector, common to, etc. Examples should be simple and involve at most one non-linear inequality, but should include both bounded and unbounded regions. Note that the case of one or more linear inequalities is specifically listed in Topic 6.

A clear sketch diagram, illustrating the relevant regions, should be drawn for each example. Regions whose algebraic description involves two or more inequalities should be understood to correspond to the common part intersection of the regions determined by each separate inequality. From Wikibooks, open books for an open world. Namespaces Book Discussion.

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