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Math Functions, Relations, Domain & RangeFunctions & Relations Home Related: Jeopardy Game-functions & relations | relations| interactive function | functions | evaluating functions | vertical line test | composition of Functions | one-to-one functions | inverse of a function | domain and range of function types  Worksheet on Functions in Math (relations, domain and range) This worksheet goes in tandem with this web page.
In math, a relation is just a set of ordered pairs.
Note: { } are the symbol for "set"
A relation is just a set of ordered pairs. There is absolutely nothing special at all about the numbers that
are in a relation. In other words, any bunch of numbers is a relation so long as these numbers come in pairs.
The domain and range of a relationThe domain is the set of all the first numbers of the ordered pairs . In other words, the domain is all of the x-values.The range is the set of the second numbers in each pair, or the y-values. Examples of the Domain and Range
Example two of the domain and range of a relation
Practice Identifying Domain and Range 
In the relation above,
the range is { -5, 31, -11, 3} What is the domain and range of the following relation?
{ (-1,2), (2, 51), (1, 3), (8, 22), (9, 51) }
Range: 2, 51, 3, 22, 51 What is the domain and range of the following relation
{ (-5,6), (21, -51), (11, 93), (81, 202), (19, 51) }
Range: 6, -51, 93, 202, 51
Interactive Relation
As the ball drops, you can see the relation of the ball's position and time. The general formula to express this relation is f(time)= positionTry changing the speed of ball's position. How does the speed effect the relation.
What makes a relation a function in Math?Functionsare a special kind of relation .At first glance, a function looks just like a relation. It's a set of ordered pairs such as { (0,1) , (5, 22), (11,9) }In mathematics, what distinguishes a function from a relation is that each x value in a function has one and only ONE y-value.
Since relation #1 has ONLY ONE y value for each x value, this relation is a function.
Practice Identifying FunctionsPractice Problems
Practice Problem one
Which relations below arefunctions? Relation #1 { (-1,2), (-4,51), (1,2), (8,-51) } Relation #2 { (13,14), (13,5) , (16,7), (18,13) } Relation #3 { (3,90), (4,54), (6,71), (8,90) } The Functions Relation #1 and Relation #3 are both functions.
Practice Problem Two
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Which relations below arefunctions?
Relation #1 { (3,4), (4,5), (6,7), (8,9) }
Relation #2 { (3,4), (4,5), (6,7), (3,9) } Relation #3 { (-3,4), (4,-5), (0,0), (8,9) } Relation #4 { (8, 11), (34,5), (6,17), (8,19) } The Functions Relation #1 and Relation #3 are functions because each x value, each element in the domain, has one and only only one y value, or one and only number in the range.
Practice Problem Three) For the following relation to be a function, X can not be what values?
{ (8, 11), (34,5), (6,17), (X ,22) }
X cannot be 8, 34, or 6.
Practice Problem Four)
For the relation below to be a function, X cannot be what values?
{ (12, 13), (-11, 22), (33, 101), (X ,22) }
X cannot be 12 or 33 .
Practice Problem Five)
For the relation below to be a function, X cannot be what values?
{ (12,14), (13,5) , (-2,7), (X,13) }
X cannot be 12, 13, or -2.
Functions & Relations Home Related: Jeopardy Game-functions & relations | relations| interactive function | functions | evaluating functions | vertical line test | composition of Functions | one-to-one functions | inverse of a function | domain and range of function types |
Graphing Calc
