Difference between revisions of "Function Command"

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<noinclude>{{Manual Page}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|function}}
; Function[Function f, Number a, Number b]: Yields a function that is identical to the original function ''f'', but whose graph is restricted to the interval [''a'', ''b''].  
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;Function( &lt;List of Numbers> )
<div class="note">'''Note:'''
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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.
* This command should be used only to restrict the display interval of a function.  To restrict the function’s domain, create a conditional function with the [[If Command]].
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:{{example|1= <div>
* Example: <tt>f(x) = Function[x^2, -1, 1]</tt> produces a function equal to ''x<sup>2</sup>'' whose graph appears only in the interval [''-1'', ''1'']. However, while <tt>g(x) = 2 f(x)</tt> will produce the function ''g(x) = 2 x<sup>2</sup>'', this function is not restricted to the interval [''-1'', ''1''].
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:*<code>Function[{2, 4, 0, 1, 0, 1, 0}]</code> yields a triangular wave between ''x = 2'' and ''x = 4''.
</div>
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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>}}
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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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:{{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>}}

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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