5.2 Relations and Functions
Identifying Relations and Functions
Relation: A set of ordered pairs.
Speed (mph)
12 24 36 48 60
Braking Distance (feet) 7 29 66 117 183
Independent Variable: Speed  input (domain)
Dependent Variable: Braking Distance  output (range)
You can list the set of ordered pairs in a relation using braces.
(12,7),(24, 29),(36,66),(48,117),(60,183)
A function is a relation that assigns exactly one output (range)
value for each input (domain) value.
Identifying Relations and Functions
One way to tell if a relation is a function is by making a mapping
diagram. Determine whether the relation is a function.
Ex1) (12, 4),(14,0),(16, 2),(18,3),(20, 2)
domain
range
12
14
16
18
20
4
2
0
3
Ex2) (0,0),(1,1),(4, 2),(1, 1),(3,0)
Identifying Relations and Functions
Vertical Line Test: If any vertical line passes through more than one
point of a graph, then the relation is not a function.
Identifying Relations and Functions
Vertical Line Test:
Function or not?
5
Ex3)
5
Ex4)
4
4
3
3
2
2
1
1
-5 -4 -3 -2 -1
1
2
3
4
5
-5 -4 -3 -2 -1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
2
3
4
5
Evaluating Functions
A function rule is an equation that describes a function.
can also be written using function notation:
Evaluating Functions
Ex5) Make a table of values for the function f(x) = 2x – 4.
Use 1, 2, 3, and 4 for the domain (input values).
input
x


domain 


output
f(x)= 2x - 4
y


 range


Evaluating Functions
Ex6) Make a table to find the range of the function rule for the
given domain.
g (n)  3  2n 2 , 3, 1,0,2,4
5.2 Relations and Functions
Homework #:35
Page 259 # 1-3,
9-12, 32-35