Difference between revisions of "Function Command"

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<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|function}}
{{command|function}}
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;Function( &lt;List of Numbers> )
; Function[Function f, Number a, Number b]: Yields a function graph, that is equal to ''f'' on the interval [''a'', ''b''] and not defined outside of [''a'', ''b''].  
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: Yields the following function: The first two numbers determine the start ''x''-value and the end ''x''-value. The rest of the numbers are the ''y''-values of the function in between in equal distances.
{{Note|1=<div>
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:{{example|1= <div>
* This command should be used only to restrict the '''display''' interval of a function. To restrict the function’s domain or use it with the [[Sequence Command|Sequence command]], create a conditional function with the [[If Command|If command]], e.g. <br/><code>f(x) = If[-1 < x < 1, x²]</code>.
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:*<code>Function[{2, 4, 0, 1, 0, 1, 0}]</code> yields a triangular wave between ''x = 2'' and ''x = 4''.
* Example: <code>f(x) = Function[x^2, -1, 1]</code> produces a function equal to ''x<sup>2</sup>'' whose graph appears only in the interval [''-1'', ''1'']. However, while <code>g(x) = 2 f(x)</code> will produce the function ''g(x) = 2 x<sup>2</sup>'' as expected, this function is not restricted to the interval [''-1'', ''1''].
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:*<code>Function[{-3, 3, 0, 1, 2, 3, 4, 5}]</code> yields a linear equation with slope ''= 1'' between ''x = -3'' and ''x = 3''. </div>}}
* This command does not work with Tools / Macros. Use the [[If Command|If command]] as above.
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; Function( <Expression>, <Parameter Variable 1>, <Start Value>, <End Value>, <Parameter Variable 2>, <Start Value>, <End Value> ): Restricts the visualization of the representative surface of a function of two variables in 3D space.
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{{betamanual|version=4.2|
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:{{Example|1=<div>The expression <code>a(x, y) = x + 0y</code> creates a function of two variables, whose graph in 3D space is the <b><u>plane</u></b> ''z'' = ''a''(''x'', ''y'') = ''x''.<br/><code>Function[u, u, 0, 3, v, 0, 2] </code> creates the function of two variables ''b''(''u'', ''v'') = ''u'',  whose graph in 3D space is the <b><u>rectangle</u></b> Polygon[(0, 0, 0), (3, 0, 3), (3, 2, 3), (0, 2, 0)] contained in plane ''z'' = ''a''(''x'',''y'') = ''x''.</div>}}
{{Note|1=From GeoGebra 4.2, Function[ <List of Numbers> ] has been added for use by the Freehand Tool. The first two numbers are the start and end of the function and the rest of the numbers are the heights. For example Function[{2, 4, 0, 1, 0, 1, 0}] makes a triangular function between x=2 and x=4}}
 
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Latest revision as of 17:15, 7 October 2017


Function( <List of Numbers> )
Yields the following function: The first two numbers determine the start x-value and the end x-value. The rest of the numbers are the y-values of the function in between in equal distances.
Example:
  • Function[{2, 4, 0, 1, 0, 1, 0}] yields a triangular wave between x = 2 and x = 4.
  • Function[{-3, 3, 0, 1, 2, 3, 4, 5}] yields a linear equation with slope = 1 between x = -3 and x = 3.
Function( <Expression>, <Parameter Variable 1>, <Start Value>, <End Value>, <Parameter Variable 2>, <Start Value>, <End Value> )
Restricts the visualization of the representative surface of a function of two variables in 3D space.
Example:
The expression a(x, y) = x + 0y creates a function of two variables, whose graph in 3D space is the plane z = a(x, y) = x.
Function[u, u, 0, 3, v, 0, 2] creates the function of two variables b(u, v) = u, whose graph in 3D space is the rectangle Polygon[(0, 0, 0), (3, 0, 3), (3, 2, 3), (0, 2, 0)] contained in plane z = a(x,y) = x.
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