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Relations. We often indicate that two numbers are related to each other using notation that we call an ordered pair.This notation pairs two numbers together using parentheses, for example, \((3, 7)\).
Example 1: Each element of the domain is being traced to one and only element in the range. However, it is okay for two or more values in the domain to share a common value in the range. That is, even though the elements 5 and 10 in the domain share the same value of 2 in the range, this relation is still a function. Example 2:
That is, g: 9 2(9) + 3. Simplifying, g: 9 21. In general, g takes a real number x, doubles it, then adds three. In symbols, we would write. g: x 2x + 3. Notice that each real number x is mapped by g to a unique number in its range. Therefore, we’ve again defined a rule that completely defines the function g.
Nov 7, 2024 · Pair. A set of two numbers or objects linked in some way is said to be a pair. The pair and is usually denoted (, ), and is generally considered to be ordered, making it a 2-tuple. In certain circumstances, pairs are also called brothers or twins.
Brackets are symbols used in pairs to group things together. When we see things inside brackets we do them first (as explained in Order of Operations). The parentheses group 3 and 2 together, and 6 and 4 together, so they get done first: Without the parentheses the multiplication is done first: With more complicated grouping we can use ...
The pair of numbers are ordered with the smaller number written first. For example, [latex](-1, 3)[/latex] means an interval on a number line starting at –1 and ending at 3. The parentheses means both of the two numbers –1 and 3 are not included in the interval, but are boundaries of the interval. Figure 3 shows this interval on a number line.
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Definition 3. A relation R is called a mapping (map), or a function, or a transformation, iff every element x \in D_ {R} has a unique R -relative, so that R [x] consists of a single element. This unique element is denoted by R (x) and is called the function value at x (under R). Thus R (x) is the only member of R [x].
