# Difference between revisions of "Inequalities"

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− | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{objects|geometric}} |

− | {{objects|geometric}} | + | GeoGebra supports inequalities in one or two variables. There are no limitations for inequalities to appear in [[File:Menu view algebra.svg|link=|16px]] [[Algebra View]], but only specific inequalities can be drawn in [[File:Menu view graphics.svg|link=|16px]] [[Graphics View]]: |

− | GeoGebra supports inequalities in one or two variables. There are no limitations for inequalities to appear in [[Algebra View]], but only specific inequalities can be drawn in [[Graphics View]]: | ||

* polynomial inequalities in one variable, e.g. ''x^3 > x + 1'' or ''y^2>y'', | * polynomial inequalities in one variable, e.g. ''x^3 > x + 1'' or ''y^2>y'', | ||

− | * | + | * quadratic inequalities in two variables, e.g. ''x^2 + y^2 + x*y ≤ 4'', |

* inequalities linear in one variable, e.g. ''2x > sin(y)'' or ''y < sqrt(x)''. | * inequalities linear in one variable, e.g. ''2x > sin(y)'' or ''y < sqrt(x)''. | ||

− | For inequality sign you can use <, >, ≤, ≥. Symbols <= and => also valid. | + | For inequality sign you can use <, >, ≤, ≥. The Symbols <= and => also valid. |

+ | Conjunction and disjunction are also supported for inequalities, e.g. ''(x>y)&&(x+y<3)'' can be drawn. | ||

− | + | In order to show the solution of an inequality as one or more intervals on the x-axis, select the ''Show on x-axis'' option in the ''Style'' tab of the [[File:Menu-options.svg|link=|16px]] [[Properties_Dialog| Properties dialog]] of the inequality. (This does not work with every inequality.) | |

− | + | Inequalities are similar to functions. You can test whether ''x'' and ''y'' satisfy inequality ''a'' by typing <code>a(x,y)</code> in the [[Input Bar]], also when ''A'' is a point, syntax <code>a(A)</code> is valid. A point can be restricted to the region given by inequality using [[PointIn Command]]. For inequality ''b'' in one variable, e.g. in ''x'', <code>Point(b)</code> yields a point restricted to the part of x-axis which satisfies inequality ''b''. |

## Latest revision as of 11:16, 12 October 2017

GeoGebra supports inequalities in one or two variables. There are no limitations for inequalities to appear in Algebra View, but only specific inequalities can be drawn in Graphics View:

- polynomial inequalities in one variable, e.g.
*x^3 > x + 1*or*y^2>y*, - quadratic inequalities in two variables, e.g.
*x^2 + y^2 + x*y ≤ 4*, - inequalities linear in one variable, e.g.
*2x > sin(y)*or*y < sqrt(x)*.

For inequality sign you can use <, >, ≤, ≥. The Symbols <= and => also valid.
Conjunction and disjunction are also supported for inequalities, e.g. *(x>y)&&(x+y<3)* can be drawn.

In order to show the solution of an inequality as one or more intervals on the x-axis, select the *Show on x-axis* option in the *Style* tab of the Properties dialog of the inequality. (This does not work with every inequality.)

Inequalities are similar to functions. You can test whether *x* and *y* satisfy inequality *a* by typing `a(x,y)`

in the Input Bar, also when *A* is a point, syntax `a(A)`

is valid. A point can be restricted to the region given by inequality using PointIn Command. For inequality *b* in one variable, e.g. in *x*, `Point(b)`

yields a point restricted to the part of x-axis which satisfies inequality *b*.