Alg 1 - Relations and Functions

Vertical Line Test

A test use to determine if a relation is a function. A relation is a function if there are no vertical lines that intersect the graph at more than one point.

dependent variable

A variable (y) that depends on one or more other variables

Relations Expressed as Mappings Express the following relations as a mapping, state the domain and range, then determine if is a function. {(-2, -1), (0, 3), (5, 4), (-2, 3)

No, it is not a function Domain: -2, 0, 5 Range: -1, 3, 4

Relations Expressed as Mappings Express the following relations as a mapping, state the domain and range, then determine if is a function. {(-1, 7), (0, -3), (1, 10), (0, 7)}

No, it is not a function. Domain: -1, 0, 1 Range: -3, 7, 10

What is the domain and range of the following relation? Is it a function? {(1, -2), (-2. 0), (-1, 2), (1, 3)}

No, it is not a function. Domain: -2, -1, 1 Range: -2, 0, 2, 3

Domain

The set of inputs or x-values

Range

The set of outputs or y-values

Independent variable

The variable that represents the input and causes the change in the dependent variable; x-axis label

If each number in the domain has an arrow to only one number in the range.

When does the mapping diagram represent a function?

Relations Expressed as Mappings Express the following relations as a mapping, state the domain and range, then determine if is a function. {(-1, 5), (0, 3), (2, 3), (3, -1)}

Yes, it is a function Domain: -1, 0, 2, 3 Range: 5, 3, -1

Draw the mapping diagram for the relation and determine whether it is a function or not. {(2, 4), (- 8, 0), (1, 5), (3, 1)}

Yes, it is a function.

What is the domain and range of the following relation? Is it a function? { (-1,2), (2, 51), (1, 3), (8, 22), (9, 51) }

Yes, it is a function. Domain: -1, 2, 1, 8, 9 Range: 2, 51, 3, 22, 51

What is the domain and range of the following relation? Is it a function? {(1, 1), (2, 2), (3, 5), (4, 10), (5, 15)}

Yes, it is a function. Domain: 1, 2, 3, 4, 5 Range: 1, 2, 5, 10, 15

definition of function

a relation that assigns exactly one output value for each input value

Relation

a set of ordered pairs: { (1,4), ( 1,5), (4,5), (3,2)}

definition of relation

a set of pairs of input and output values

Express the relation as a table and a graph. Then state the domain and range {(4, −2), (−1, 1), (2, −3), (3, 0)}

domain: {-1, 2, 3, 4} range:{-3, -2, 0, 1}

Express the relation as a table and a graph. Then state the domain and range. {(3, −4), (2, 0), (−4, −1), (0, −3)

domain: {-4, 0, 2, 3} range:{-4, -3, -1, 0}

Express the relation as a table and a graph. Then state the domain and range {(3, 4), (1, −2), (4, −1), (2, 2)}

domain: {1, 2, 3, 4} range:{-2, -1, 2, 4}