Algebra 2
Name ______________________________
WS 1.1: Relations, Functions, Domain, and Range
Class Period _______________
State the domain and range of each relation, then state whether the relation is a function.
Explain your reasoning.
1. {(-1, 2), (3, 10), (-2, 20), (3, 11)}
D: {-2, -1, 3}, R: {2, 10, 11, 20}
The relation is NOT a function because the x-value (input) 3 has more than one y-value (output).
2. {(0, 2), (13, 6), (2, 2), (3, 1)}
D: {0, 2, 3, 13}, R: {1, 2, 6}
The relation IS a function because each x-value (input) has only 1 y-value (output).
3. {(1, 4), (2, 8), (3, 24)}
D: {1, 2, 3}, R: {4, 8, 24}
The relation IS a function because each x-value (input) has only 1 y-value (output).
Given that x is an integer, state the relation representing each of the following by listing a
set of ordered pairs.
4. y = 3x2 – 5, where 0<x<5
{(1, -2), (2, 7), (3, 22), (4, 43)}
5. y = 4x – 5, where -1<x<3
{(0, -5), (1, -1), (2, 3)}
x  5 , where  1  x  2
{(-1, 2), (0, 5 ), (1, 6 ), (2,
6. y =
7 )}
Given f(x) = x  3  2 , find each of the following: You MUST show work for credit!
7. f(6) = 1
8. f(13) = 2
Given each mapping diagram, write the corresponding set of ordered pairs and determine
whether each is a function or relation. Explain your reasoning.
9.
10.
1
0
-1
1
2
3
4
-5
0
7
8
-6
9
12
Ordered pairs:
{(1, 1), (1, 2), (0, 3),(-1, 4)}
Function or Relation? __relation____
Reason: The x-value (input) 1 has more
than one y-value (output).
Ordered pairs:
{(-5, -6), (0, 9), (7, 9), (8, 12)}
Function or Relation? __function_____
Reason: Each x-value (input) has only 1 yvalue (output).
Name the domain and range of each function.
y
y

11.

13.






x








x


















Domain: x  R or  ,  
Domain: x  R or  ,  
Range: y  0 or 0, 
Range: y  2 or  , 2
y
12.
y
14.








x
x






















Range: y  0 or 0, 



Domain: x  0 or 0, 

Domain: x  R or  ,  
Range: y  R or  ,  
Use a vertical line test to determine which graphs represent functions. Explain.
15.
16.
17.
Function or Relation_function_
Function or Relation__relation
Function or Relation_relation_
Reasoning: A vertical line does not Reasoning: A vertical line touches Reasoning: A vertical line
touch more than one point at any time.
more than one point.
touches more than one point.
Use a vertical line test to determine which graphs represent functions. Explain.
18.
19.
20.
Function or Relation_ function
Reasoning: A vertical line does not
touch more than one point at any time.
Function or Relation relation
Reasoning: A vertical line touches
more than one point.
Function or Relation_ function
Reasoning: A vertical line does
not touch more than one point.