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Represent Relations and Functions

+Relation A relation is a mapping, or pairing , of input values with output values.

The set of input values in the domain.

The set of output values is the range.

+Representing Relations

A relation can be represented in the following ways:

Ordered pairs

Table

Graph

Mapping Diagram

+Ordered Pairs

(-2, 2), (-2, -2), (0, 1), (3,1)

Domain (the x values): {-2, 0,

3}

Range (the y values): {-2, 1, 2}

+Table

x y

-4 2

-2 2

1 6

4 7

Domain:

{-4, -2, 1, 4}

Range:

{2, 6, 7}

+Graph

Domain:

{-2, -1, 2, 3}

Range:

{-3, -2, 1, 3}

+Mapping

Domain:

{-2, -1, 1, 2, 3}

Range:

{-3, -2, 1, 3}

+Is the relation a function?

A relation is a function if each input has exactly one output…

“the x’s can’t repeat”

+Function?? Function Not a Function

+Vertical Line Test A relation is a function if and only if no vertical line intersects the graph of the relation at more then one point.

Function Not a Function

+Equations in Two Variables

An equation in two variables is an equation such as y = 3x -5

“x “ is the input variable and is called the independent variable. It represents the independent quantity.

“y” is the output variable and is called the dependent variable. It represents the dependent quantity.

“y depends on x”

+Solution An ordered pair (x, y) is a solution of

an equation in two variables if substituting x and y in the equation produces a true statement.

Ex: (2, 1) is a solution to y = 3x – 5

because 1 = 3(2) – 5

The graph of an equation in two variables is the set of all points (x, y) that represent solutions of the equation.

+Linear Functions

A linear function can be written in the form y = mx + b

The graph of a linear function is a line

y = mx + b ~ x-y notation

f(x) = mx + b ~ function notation

(‘f of x” or “the value of f at x”)

Ex: f(x) = 5x + 8 f(-4) = 5(-4) + 8 = -12 The value of the function at x = -4 is 12

+Discrete and Continuous FunctionsThe graph of a discrete function consists of separate points.

The graph of a continuous function is “unbroken”

+Slope

Watch and listen to the following links:

Introduction to slope

Parallel and Perpendicular Lines