2-1, Relations and Function Notes:



2-1, Relations and Function Notes:

I.) Ordered Pairs and Domain and Range-

Ordered pairs are data or other information presented as two numbers in parenthesis set apart by a comma. Example: (3,2)

In algebra, we usually use this in graphing. When we use ordered pairs in graphing we usually call them coordinates.

There are many different ways we can present coordinates. One way of presenting coordinates is on the Cartesian Coordinate Plane. This has an X – axis and a Y – axis.

In the following, find the coordinates of the points.

A (

B (

C (

D (

Sometimes, coordinates are correlated or associated with each other. If the numbers linked in some way we say there is a relation. In any relation, there is a domain and range. The domain is the set of all first coordinates and the range is the set of all second coordinates.

What is the domain and range of these points?

( 2 , 3 ) , ( 1 , 4 ) , ( -10 , 7 ) , (-1 , -2 ) , ( 10 , 5 )

Domain:_______________

Range: ________________

**Notes:

II. Defining Functions

A function is a special type of relation in which each element (or number) in the domain is paired with one, and exactly one, element in the range.

Mapping is a technique in which we draw arrows from the domain values to each corresponding value in the range.

{ ( 2,1) , (-3, 2) , (4, 5)}

Domain Range

[pic][pic][pic]

Notice that each element in the domain has only one arrow heading to a value in the range. A function cannot have more than one arrow from each element in the domain mapping to the range. This is by definition.

In addition, a one-to-one function is one in which there is only one arrow from each element in the domain to each element in the range.

In the following, tell whether it is a function or not.

i.) ii.)

iii.) iv.)

III. Vertical Line Test

One technique that is helpful in finding whether or not a graph is a function or not is the vertical line test. A vertical line is one that moves up and down (a horizontal line moves left and right).

The vertical line test states that if you can draw a vertical line anywhere on a graph where the line intersects two or more points on the graph, the relation IS NOT a function.

Example:

In the first graph, it is a function In the second graph, it IS NOT a function

because a vertical line anywhere on because a vertical line at x= -4 would result

this graph would result in only 1 inter- in 3 intersections.

section.

[pic]

In the following graphs, use the vertical line test to tell whether or not the relation is defined as a function.

i.) ii.)

IV. Independent and Dependent Variables

A good way to remember the difference between dependent and independent variables is this: The independent variable does not depend on any other value whereas the dependent variable depends on the independent variable.

We routinely use the x variable as the independent variable and the y variable as the dependent variable. However, you might see the independent variable as t (time) or some other value. The dependent variable might also be in another notation.

Function notation is the way in which we write down equations. We use this notation because it is convenient in finding values.

In function notation, we define the function name with one variable (most of the time it is f) and the dependent with another variable (most of the time it is x).

Example: f(x) = 2x + 3

In this example, the function is called f(x) and 2x + 3 is the operations we do to find f(x).

For instance, using the equation we have above find f(3).

f(3) = 2(3) + 3 = 9 so…. f(3) = 9

As you can see, function notation is good for stating what we are substituting in for the independent variable. When I write f(3) you know that you are substituting 3 for every place where the independent variable is located.

In the following, change the equation to function notation.

Equation Function Notation Find Value For….

i.) [pic] f(2) =

ii.) [pic] f(6) =

iii.) [pic] f(-2) =

iv.) [pic] f(1) =

v.) [pic] f(3) =

vi.) [pic] f(-2) =

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

1

2

5

2

-3

4

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download