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)

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)
 * Graphofyequals2x.png


 * 1) /Slope-intercept form/

Two-point form
Two points also uniquely determine a line. Given points $$(x_1,y_1)$$ and $$(x_2,y_2)$$, we have the equation

$$ y - y_1 = \frac{y_2-y_1}{x_2-x_1}(x-x_1). $$

This presentation is in the two-point form. It is essentially the same as the point-slope form except we substitute the expression $$\frac{y_2-y_1}{x_2-x_1}$$ 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)
 * Qfunction.png

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)