Notes: Relations and Functions (Page 72)



Notes: Relations and Functions (Page 72) |Name: Period: Date: | |A ________________ is a ___________ or _____________ of input values with output values.

The set of input values is the ______________. The set of output values is the _____________.

Relations can be represented in the following ways.

Ordered Pairs Table Graph Mapping

(-2, 2)

(-2, - 2)

( 0, 1)

( 3, 1)

Consider the relation given by the following ordered pairs (-2, 1), ( -1, -4), ( 0, 5), ( 1, -3), (3, 5).

a. Identify the domain and range. _____________________________________________

b. Represent the relation using a graph and a mapping diagram.

mapping

______________________________________________________________________________A _____________ is a relation for which each ____________ has exactly one ______________.

Consider the examples we have already used. Is either of them a function? Why or why not?

input output input output

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

Discrete and Continuous Functions The graph of a ____________function consists of separate points.

The graph of a ______________ function is unbroken.

Using the vertical line test, determine whether or not the following graphs are graphs of functions. Then, identify the domain, range and whether the graph is discrete or continuous.

[pic] [pic] [pic]Function? yes or no Function? yes or no Function? yes or no

domain ____________ domain _____________ domain _____________

range ______________ range _______________ range_______________

discrete or continuous discrete or continuous discrete or continuous

[pic] [pic][pic]

Function? yes or no Function? yes or no Function? yes or no

domain ____________ domain _____________ domain _____________

range ______________ range _______________ range_______________

Set notation [pic]This is pronounced as "the set of all x, such that x is less than 3.

-----------------------

|x |y |

|-2 |2 |

|-2 |-2 |

|0 |1 |

|3 |1 |

[pic]

Input

output

[pic]

-2

0

3

2

-2

1

[pic]

[pic]

[pic]

2

-2

1

-2

0

3

[pic]

-2

-1

0

1

3

-4

-3

1

5

[pic]

y

x

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