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Representations of Multivariate Functions

Tabular Data

The table below lists the 2004 tax owed for a married couple filing jointly with the given AGI and number of children.  It assumes that the filers claim the standard deduction.  It ignores all variables other than number of children.  This includes the Alternative Minimum Tax and the Earned Income Credit.

 Number of Children  0 1 2 3 4 5 6 7
 AGI                 
 $               -    $           -    $ (1,000.00)  $ (2,000.00)  $ (3,000.00)  $ (4,000.00)  $(5,000.00)  $(6,000.00)  $(7,000.00)
 $      5,000.00  $           -    $ (1,000.00)  $ (2,000.00)  $ (3,000.00)  $ (4,000.00)  $(5,000.00)  $(6,000.00)  $(7,000.00)
 $    10,000.00  $           -    $ (1,000.00)  $ (2,000.00)  $ (3,000.00)  $ (4,000.00)  $(5,000.00)  $(6,000.00)  $(7,000.00)
 $    15,000.00  $           -    $ (1,000.00)  $ (2,000.00)  $ (3,000.00)  $ (4,000.00)  $(5,000.00)  $(6,000.00)  $(7,000.00)
 $    20,000.00  $     410.00  $    (900.00)  $ (2,000.00)  $ (3,000.00)  $ (4,000.00)  $(5,000.00)  $(6,000.00)  $(7,000.00)
 $    25,000.00  $     910.00  $    (400.00)  $ (1,710.00)  $ (3,000.00)  $ (4,000.00)  $(5,000.00)  $(6,000.00)  $(7,000.00)
 $    30,000.00  $  1,410.00  $     100.00  $ (1,210.00)  $ (2,520.00)  $ (3,830.00)  $(5,000.00)  $(6,000.00)  $(7,000.00)
 $    35,000.00  $  2,150.00  $     685.00  $    (710.00)  $ (2,020.00)  $ (3,330.00)  $(4,640.00)  $(5,950.00)  $(7,000.00)
 $    40,000.00  $  2,900.00  $  1,435.00  $     (30.00)  $ (1,495.00)  $ (2,830.00)  $(4,140.00)  $(5,450.00)  $(6,760.00)
 $    45,000.00  $  3,650.00  $  2,185.00  $     720.00  $    (745.00)  $ (2,210.00)  $(3,640.00)  $(4,950.00)  $(6,260.00)
 $    50,000.00  $  4,400.00  $  2,935.00  $  1,470.00  $        5.00  $ (1,460.00)  $(2,925.00)  $(4,390.00)  $(5,760.00)
 $    55,000.00  $  5,150.00  $  3,685.00  $  2,220.00  $     755.00  $    (710.00)  $(2,175.00)  $(3,640.00)  $(5,105.00)
 $    60,000.00  $  5,900.00  $  4,435.00  $  2,970.00  $  1,505.00  $      40.00  $(1,425.00)  $(2,890.00)  $(4,355.00)
 $    65,000.00  $  6,650.00  $  5,185.00  $  3,720.00  $  2,255.00  $     790.00  $   (675.00)  $(2,140.00)  $(3,605.00)
 $    70,000.00  $  7,400.00  $  5,935.00  $  4,470.00  $  3,005.00  $  1,540.00  $      75.00  $(1,390.00)  $(2,855.00)
 $    75,000.00  $  8,250.00  $  6,685.00  $  5,220.00  $  3,755.00  $  2,290.00  $    825.00  $   (640.00)  $(2,105.00)
 $    80,000.00  $  9,500.00  $  7,725.00  $  5,970.00  $  4,505.00  $  3,040.00  $ 1,575.00  $    110.00  $(1,355.00)
 $    85,000.00  $10,750.00  $  8,975.00  $  7,200.00  $  5,425.00  $  3,790.00  $ 2,325.00  $    860.00  $   (605.00)
 $    90,000.00  $12,000.00  $10,225.00  $  8,450.00  $  6,675.00  $  4,900.00  $ 3,125.00  $ 1,610.00  $    145.00
 $    95,000.00  $13,250.00  $11,475.00  $  9,700.00  $  7,925.00  $  6,150.00  $ 4,375.00  $ 2,600.00  $    895.00
 $  100,000.00  $14,500.00  $12,725.00  $10,950.00  $  9,175.00  $  7,400.00  $ 5,625.00  $ 3,850.00  $ 2,075.00

The Topographical Map

This topographical map is courtesy of Topozone.com (a second example is Longmire).

Algebraic Contour Plots

A webMathematica Contour Plotter, was formerly found here.  Note that the lighter the shading, the higher the point.

The Weather Map (Showing isotherms).

This weather map (from 02/23/05) is courtesy of the USA Today.

 

Dusty Wilson
Mathematics Instructor
Highline Community College
the home page of ... Dusty Wilson

  last modified December 16, 2010