Arithmetic Course/Function Definition

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Function[edit | edit source]

Function is a mathematical expression representing the relation of one quantity with another quantity. For example

  1. Function of one variable f(x)
  2. Function of two variables f(x,y)
  3. Function of three variables f(x,y,z)

Basic Functions[edit | edit source]

Straight Line Function[edit | edit source]

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)
Graphofyequals2x.png
  1. Slope-intercept form

Two-point form[edit | edit source]

Two points also uniquely determine a line. Given points and , we have the equation

This presentation is in the two-point form. It is essentially the same as the point-slope form except we substitute the expression for m.

Parabola Function[edit | edit source]

f(x) = x2

y = x2
x | -2 -1 0 1 2
y | 4 -1 0 1 4
A function of a parabola that goes through point (0,0)
Qfunction.png

Hyperbole Function[edit | edit source]

f(x) = x3

y = x3
x | -2 -1 0 1 2
y | -8 -1 0 1 8
A function of a hyperbola that goes through point (0,0)