Arithmetic Course/Function Definition

Function

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

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)

Two-point form

Two points also uniquely determine a line. Given points ${\displaystyle (x_{1},y_{1})}$ and ${\displaystyle (x_{2},y_{2})}$, we have the equation

${\displaystyle y-y_{1}={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}(x-x_{1}).}$

This presentation is in the two-point form. It is essentially the same as the point-slope form except we substitute the expression ${\displaystyle {\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}}$ for m.

Parabola Function

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)

Hyperbole Function

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)