# Relations and functions

By Nicolas Mastandrea RELATIONS AND FUNCTIONS The relation A relation is just a set of ordered pairs. There is absolutely nothing special at all about the numbers that are in a

relation. In other words, any bunch of numbers is a relation so long as these numbers come in pairs. The function In mathematics, what distinguishes a function from a relation is that each x value in a

function has one and only ONE yvalue. Categories of functions Constant function Direct variation linear function Partial variation linear function Rational function Quadratic function

The constant function The rate of change is constant and equal to 0. On a cartesian graph, it is a straight horizontal line parallel to the x-axis. Rules: y=b or f(x)=b Direct variation linear

function The rate of change is constant! The y variable is proportional to the x variable The Cartesian graph is a straight line passing through the origin, and is not parallel to an axis. Rules: y=ax or f(x)=ax

Partial variation linear function The rate of change is constant! The y variable is not proportional to the x variable. The Cartesian graph is a straight line that does not pass through the origin

and is not parallel to an axis. Rules: y=ax+b or f(x)=ax+b The rational function The rate of change is not constant. The product of the variables is constant. The Cartesian graph is a curve that

gradually approaches the axes. Rules: y= a/x or f(x)= a/x Quadratic function The rate of change is not constant Y is proportional to the square of x The complete graph is a curve called a parabola.

Rules: y = ax2+bx+c or f(x) = ax2+bx+c

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