1. Formalizing Relations and Functions
Lesson 28

2. Objective
HSF-IF.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.

3. Definitions
A relation is a pairing of numbers in one set, with the numbers of another set.
The domain, is the set of all possible x values of a relation.
The range, is the set of all possible y values of a relation.
A function is a relation such that all domain values only have one range value.

4. Example; Domain and Range
Identify the domain and range of each relation. Then determine if the relation is a function.
{(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)}
Domain: {-2, 0, 4, 5}
Range: {0.5, 2.5, 6.5}
Function because each x value has only one y value matched with it.

5. Example; Find Domain and Range
x can be any value between -6 and 6, not including -6.
y can be any value between -2 and 6.
-6 < x ≤ 6
-2 ≤ x ≤ 6
(-6, 6]
[-2, 6]

6. Example; Find Domain and Range
x can be any value except 0.
y can be any value.
x < 0 or
x > 0
-∞ ≤ x ≤ ∞
(-∞, ∞)
(-∞, 0) or
(0, ∞)

7. #28: Formalizing Relations & Functions
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