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Math functions, relations, domain & range
This document discusses math functions, relations, and their domains and ranges. It provides examples of relations and explains that the domain is the set of first numbers in ordered pairs, while the range is the set of second numbers. A function is defined as a relation where each x-value has only one corresponding y-value. It compares examples of relations that are and are not functions and describes how to evaluate functions by inserting values. Tests for identifying functions like the vertical line test are also outlined.
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Math functions, relations, domain & range
- 1. Math Functions, Relations,Domain & RangeBy Ms. R. Scott
- 2. In math, arelation 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 andRange of a RelationThe domainis the set of all the first numbers of the ordered pairs . In other words, the domain is all of the x-values.
- 4. RANGEThe range isthe set of the second numbers in each pair, or the y-values.
- 5. Examples of thedomain 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 arelation 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 tworelations on the belowSince 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 inmath 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 LineTest 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.
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- 11. FUNCTION FAMILIESPOLYNOMIAL FUNCTIONS