View source for Arithmetic Course/Function Definition

==Function==
Function is a mathematical expression representing the relation of one quantity with another quantity. For example 
# Function of one variable f(x) 
# Function of two variables f(x,y) 
# Function of three variables f(x,y,z)

==Basic Functions==
===Straight Line Function===
''f(x) = x''
: y = x
:  x | -2 -1 0 1 2
:  y | -2 -1 0 1 2
: ''A function of a straight line that goes through point (0,0)''
:[[File:Graphofyequals2x.png|200px]]

# [[/Slope-intercept form/]]

==Two-point form==
Two points also uniquely determine a line.  Given points <math>(x_1,y_1)</math> and <math>(x_2,y_2)</math>, we have the equation
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<math> y - y_1 = \frac{y_2-y_1}{x_2-x_1}(x-x_1). </math>
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This presentation is in the '''two-point form'''.  It is essentially the same as the point-slope form except we substitute the expression <math>\frac{y_2-y_1}{x_2-x_1}</math> for ''m''.

===Parabola Function===
''f(x) = x<sup>2</sup>''
: y = x<sup>2</sup>
:  x | -2 -1 0 1 2
:  y | 4 -1 0 1 4
: ''A function of a parabola that goes through point (0,0)''
:[[File:Qfunction.png|200px]]

===Hyperbole Function===
''f(x) = x<sup>3</sup>''
: y = x<sup>3</sup>
:  x | -2 -1 0 1 2
:  y | -8 -1 0 1 8
: ''A function of a hyperbola that goes through point (0,0)''

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