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Math Functions, Relations, Domain & Range<br />By <br />Ms. R. Scott<br />
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In math, a relation is just a set of ordered pairs Note: { } are the symbol for "set" <br />Some Examples of Relations include { (0,1) , (55,22), (3,-50) } <br />{ (0, 1) , (5, 2), (-3, 9) } { (-1,7) , (1, 7), (33, 7), (32, 7) }<br />
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The Domain and Range of a Relation<br />The domainis the set of all the first numbers of the ordered pairs . In other words, the domain is all of the x-values. <br />
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RANGE<br />The range is the set of the second numbers in each pair, or the y-values.<br />
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Examples of the domain and range of a relation. <br />In the relation above the domain is { 0, 3, 90 } And the range is { 1, 22, 34 }<br />
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What makes a relation a function in Math? <br />In mathematics, what distinguishes a function from a relation is that each x value in a function has one and only ONE y-value. <br />Some people find it helpful to think of the domain and range as people in romantic relationships. If each number in the domainis a person and each number in therangeis a different person, then a function is when all of the people in the domain have 1 and only 1 boyfriend/girlfriend in the range. <br />
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Compare the two relations on the below<br />Since relation #1 has ONLY ONE y value for each x value, this relation is a function. On the other hand, relation #2 has TWO distinct y values '2' and '4' for the same x value of '1'. Therefore, relation #2 does not satisfy the definition of a mathematical function. <br />
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Evaluating Functions in math <br />To evaluate a function, we insert a given x value, a number in the domain, and see what number we get, which is a number in a range. Some examples: f(x) = 2x <br />To evaluate f(4) f(4) = 2(4) = 8 We just evaluated f(x) for the value x = 4.<br />
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The Vertical Line Test The vertical Line test is a wy to determine whether or not a relation is a function. The vertical line test simply states that if a vertical line intersects the relation's graph in more than one place, then the relation is a NOT a function. <br />Relation #2 does not pass the vertical line test. <br />