By: IsaBella Combs

Section One: Relation and Functions

Domain: a set of all first coordinates. (x-coordinates)Range: a set of all second coordinates.(y-coordinates)Relation: set of ordered pairs.Ordered Pair: a pair of coordinates written in (x,y) formFunction: a relation in which exactly each element off the domain is paired with exactly one element of the domain.One-To-One: Function: function were each element of the range is paired with exactly one element of the domain.

Vocabulary:

Example of ordered pairs:

Domain and x-coordinate

Range andy-coordinate

X

Y

2

4

(6,4) , (2,-4) , (8,1) , (0,3) X Y

6 4

2 -4

8 1

0 3

* This is a one-to-one function because all the x elements and the y elements match up!

Linear equations

* A linear equation has no operations other than addition, subtraction, and multiplication of a variable by a constant.* A variable cannot be under a radical.The graph of a linear equation is always a line.* A linear equation cannot contain variables with exponents greater than one.* The variables cannot be multiplied together or appear in a denominator.

Linear Equation Example:

4x + 4y = 8

First step is to isolate "x" to one side of the equation by adding 4y to both sides:

4x - 4y + 4y = 8 + 4y4x = 8 + 4y

Second step is to divide both sides by 4:

4x / 4 = (8 + 4y) / 4x = 2 + y

Check your work with the original equation

4 * (2 + y) - 4y = 88 + 4y - 4y = 88 = 8

A linear function is a function whose ordered pairs satisfy a linear equation.

Linear Functions:

Slope = RiseRun

The slope of a line is the ratio of the change in y-coordinates to the corresponding change in x-coordinates.Rate of change measures how much a quantity changes, on average, relative to the change in another quantity, often time.

Slope Examples: