Coordinate System Review By Mrs. Swanberg 2002

(left or right, up or down) (x, y) (left or right, up or down) (run, jump) (domain, range)

Plot the following ordered pairs. B(4, -6) C(-6, 2) D(6, 2) E(-4, -6) F(0, 6) Connect the points in alphabetical order.

Quadrants I II x III IV y

Next 2 clean pages in your notebook!

Relations and Functions

Relation Any set of ordered pairs. For each first member there may be MANY second members.

Domain The possible set of all the input values for the independent variable in a given situation The set of first coordinates.

Range The possible set of all the output values for the dependent variable in a given situation. The set of second coordinates.

2 Domain 7 + 5 Range

Annual Household Waste Country Annual Domestic Waste Equivalent per Person (lbs) France 15,500 634 Great Britain 15,816 620 Japan 40,225 United States 200,000 1925 West Germany 20,780 741 {(15500, 634), (15816,620), (40225, 634), (200000, 1925), (20780, 741)}

Annual Household Waste Domain First coordinate x-value 15,500 15,816 40,225 200,000 20,780 Range Second coordinate y-value 634 620 1925 741

x y 1 -1 3 4 7 {(1, -1), (1, 3), (4, 7), (-1, 7)} Domain {1, 4, -1} Express the relation shown in each table as a set of ordered pairs. Then state the domain and range of the relation. x y 1 -1 3 4 7 {(1, -1), (1, 3), (4, 7), (-1, 7)} Domain {1, 4, -1} Range {-1, 3, 7}

x y 2 3 6 -1 {(2, 3), (6, -1), (2, -1)} Domain {2, 6} Range {3, -1} Express the relation shown in each table as a set of ordered pairs. Then state the domain and range of the relation. x y 2 3 6 -1 {(2, 3), (6, -1), (2, -1)} Domain {2, 6} Range {3, -1}

Function A relation in which for each first member there is one and only one second member.

Vertical Line Test Can be used to determine if a relation is a function. For every function, the vertical line passes through only ONE point on the graph.

Use the vertical line test to determine if the relations on the next 2 slides are functions.

AND A RELATION Function

A RELATION NOT A FUNCTION

Graph each relation. Then determine if each relation is a function. x -1 4 5 y -4 -5 Yes; it is a function because each element of the domain is paired with exactly one element in the range.

A Function {(-1, -1), (0, 0), (4, -4), (5, -5)} -1 -1 -4 4 -5 5 Range Domain -1 -4 -5 -1 4 5

Graph each relation. Then determine if each relation is a function. x 1 2 y 4 -2 -4 No; it is not a function because the element 1 in the domain maps to both 4 and -2 in the range.

1 2 Not a Function {(1, 4), (0, 0), (1, -2), (2, -4)} 4 -2 -4 Range Domain 4 -2 -4 1 2

Is this a function? {(1, -2), (0, 0), (2, -2)} Range Domain 1 2 -2

Some relations are functions.

All functions are relations.