2. In math, a relation is just a set of ordered pairs Note: { } are the symbol for "set" Some Examples of Relations include { (0,1) , (55,22), (3,-50) } { (0, 1) , (5, 2), (-3, 9) } { (-1,7) , (1, 7), (33, 7), (32, 7) }
3. The Domain and Range of a Relation The domainis the set of all the first numbers of the ordered pairs . In other words, the domain is all of the x-values.
4. RANGE The range is the set of the second numbers in each pair, or the y-values.
5. Examples of the domain and range of a relation. In the relation above the domain is { 0, 3, 90 } And the range is { 1, 22, 34 }
6. What makes a relation a function in Math? In mathematics, what distinguishes a function from a relation is that each x value in a function has one and only ONE y-value. 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.
7. Compare the two relations on the below 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.
8. Evaluating Functions in math 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 To evaluate f(4) f(4) = 2(4) = 8 We just evaluated f(x) for the value x = 4.
9. 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. Relation #2 does not pass the vertical line test.
