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math - relation, function, domain, range











































Define a relation.

Define a function.

Define the domain. Is this the dependent of independent variable?

Define the range. Is this the dependent of independent variable?

Complete an (x,y) table for the following equation: y = 2x – 2

Rewrite the values from your table as a set of ordered pairs.

Graph the ordered pairs.

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Jun 26, 2012
Relation, function, domain, and range
by: Staff

Define a relation.

A relation is ANY set of ordered pairs (x,y).

The first object in the ordered pair (the “x”) is related to the second object (the “y”) in the ordered pair. The object can be a number or something else.

Multiple first objects (multiple values of “x”) can be related to the same second object (the “y”).

Both of the following examples are valid relations:

(1,5), (2,6), (3,7), (4,8), (5,9)

(1,6), (2,6), (3,6), (4,8), (5,9)




Define a function.

A function is a relation with one important restriction.

Multiple first objects (multiple values of “x”) CANNOT be related to the same second object (the same “y”).


The following example is a FUNCTION:

(1,5), (2,6), (3,7), (4,8), (5,9)



The following example is NOT a FUNCTION:

(1,6), (2,6), (3,6), (4,8), (5,9)




Define the domain. Is this the dependent of independent variable?

The domain is the set of all the possible objects which are the first in a set of ordered pairs. If the ordered pairs are (x,y), all possible “x” objects are the domain.

The following set of ordered pairs is the same example used above:

(1,5), (2,6), (3,7), (4,8), (5,9)

The domain of this set of ordered pairs is: 1, 2, 3, 4, 5



The objects in the domain are independent variables.




Define the range. Is this the dependent of independent variable?


The range is the set of all the possible objects which are the second in every set of ordered pairs. If the ordered pairs are (x,y), all possible “y” objects are the range.

The following set of ordered pairs is the same example used above:

(1,5), (2,6), (3,7), (4,8), (5,9)

The range of this set of ordered pairs is: 5, 6, 7, 8, 9


The objects in the range are dependent variables.





Complete an (x,y) table for the following equation: y = 2x - 2

x, y = 2x - 2

0, 2*0 - 2 = -2
1, 2*1 - 2 = 0
2, 2*2 - 2 = 2
3, 2*3 - 2 = 4
4, 2*4 - 2 = 6
5, 2*5 - 2 = 8


x, y
0, -2
1, 0
2, 2
3, 4
4, 6
5, 8



Rewrite the values from your table as a set of ordered pairs.

{(0, -2) (1, 0) (2, 2) (3, 4) (4, 6) (5, 8)}




Graph the ordered pairs.


Open the following link to view the graph:


(1) If your browser is Firefox, click the following link to VIEW the VENN Diagram; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page

http://www.solving-math-problems.com/images/plot-ordered-pairs-2012-06-26.png




Thanks for writing.

Staff
www.solving-math-problems.com


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