1. 4.6 – Formalizing Relations and Functions

2. Vocab, Vocab, Vocab!!
Relation – a pairing of numbers in one set with numbers in another set.
Domain – the set of x-values of a relation
Range – the set of y-values of a relation

3. Identify the domain and range of each relation
Identify the domain and range of each relation. Represent the relation with a mapping diagram. Is the relation 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}
Domain Range -2 4 5
0.5
2.5
6.5
Yes, the relation is a function because each domain value is mapped to one range value.

4. Identify the domain and range of each relation
Identify the domain and range of each relation. Represent the relation with a mapping diagram. Is the relation a function?
{(6, 5), (4, 3), (6, 4), (5, 8)}
Domain Range
DOMAIN: {4, 5, 6}
RANGE: {3, 4, 5, 8} 3 4 5 8 4 5 6
No, the relation is not a function because the domain value 6 is mapped to two range values.

5. And more vocab!
4. Vertical Line Test – another way to decide if a relation is a function.
If a vertical line crosses a graph only once, then the relation is a function
If a vertical line crosses a graph more than once, then the relation is not a function.

6. Are the following relations functions? Use the vertical line test.

7. Just one more vocab word!
5. Function Notation: replacing y with f(x) in an equation that represents a function.
Example: f(x) = -3x + 1

8. Find the range for each function for the given domain.
f(x) = 5x – 2; {-1, 3, 10}
f(x) = |x – 2|; {-3, 0, 4}

9. Homework
Page 272 # 8 – 15, 18 – 21,