1. Set of first coordinates in an ordered pair. (the x values) Range:
Section 5-2 Relations and Functions SPI 23C: determine the domain/range of a function represented by the graph of real-world situations
Objectives:
Identify relations and functions
Evaluate Functions
Vocabulary
Domain:
Set of first coordinates in an ordered pair. (the x values)
Range:
Set of second coordinates in a ordered pair (the y values)
Relation:
Set of all ordered pairs; x value may be repeated
Function f(x) or y:
a relation that assigns exactly one value in the range to each value in the domain. (x value may not be repeated)

2. Write values from table as an ordered pair
Domain and Range
Giraffes
Age (years
Height (meters) 18
4.25 20
4.40 21
5.25 14
5.00
4.85
Write values from table as an ordered pair
Domain
Range
Domain
Age Height
Range
(18, )
(20, )
(21, )
(14, )
(18, )
Domain
Range
x-values in a table or
ordered pair
write values only once in order from least to greatest
D={14, 18, 20, 21}
y-values in a table or
ordered pair
write values only once in order from least to greatest
R={4.25, 4.40, 4.85, 5.00, 5.25}

3. Relation and Functions
Giraffes
Age (years
Height (meters) 18
4.25 20
4.40 21
5.25 14
5.00
4.85
Not a Function
(x-value is repeated)
Relation
Function
Set of all ordered pairs
x-value may be repeated
The (age, height) ordered pair form a relation.
A special relation
x-value may not be repeated
The (age, height) ordered pair does NOT form a relation.

4. Determine if a Relation is a Function (Vertical Line Test)
Use to determine if a relation is a function
Plot the data from a table of values, on a coordinate plane.
x-values
(Domain)
y-values
(Range) 3 -2 1 -1 -3 2
Pass a pencil, vertically, across the graph.
If it passes through only one point at a time, then it is a function.

5. Determine if a Relation is a Function (Mapping Diagram)
Also used to determine if a relation is a function
The relation is
NOT
a function
List domain and range values in order
x-values
(Domain)
y-values
(Range) 3 -2 1 -1 -3 2
Domain
Range -3 -2 3 -2 -1 1 2
Draw arrow from domain values to corresponding range values
Notice the domain value 3 corresponds to 2 range values

6. Determine if a Relation is a Function (Mapping Diagram)
Which mapping diagram is a function? 11 12 13 20
Domain -2 -1 7
Range -2 -1 4
Domain 1 3
Range
This is a
function
This is NOT
a function

7. Investigate Functions
The Function Machine
INPUT
(domain, x value)
Domain
(x value)
Range
(y value)
x = 0 4
Function rule
f(x) = 2x + 4
y = 2x + 4 1 6
f(1) = 2(1) + 4
f(0) = 2(0) + 4
x = 1
Output
(range, y value)
f(1) = 6
f(0)= 4
Each x value has one and only one y value.

8. Do Now A Little Practice 1. Evaluate the function rules:
1. f(n) = -3n – 10 for n = y = -2x2 + 7 for x = - 4
2. What is the range of the function in problem 1 for the domain {0, 1, 2}?
f(6) = -3(6) – 10
= -18 – 10
= -28
y = -3(-4)2 + 7
= -3(16) + 7
= -41
f(0) = -3(0) – 10
= 0 – 10
= -10
f(1) = -3(1) – 10
= -3 – 10
= -13
f(2) = -3(2) – 10
= -6 – 10
= -16
The range is {-16, -13, -10}.