Name
Class
2-6
Date
Enrichment
Formalizing Relations and Functions
The relation between the domain and range can be a function.
A function is a special type of relation in which each value in the domain
is paired with exactly one value in the range.
Relations and functions may be represented in various forms. For example, verbal descriptions,
tables, mapping diagrams, scatter plots and set notation.
1. Johnson County officials are preparing the budget for the coming fiscal year. Since the
national census is only taken every ten years they have decided to take one of their own
to obtain accurate population numbers of the six cities in the county. To date they have
collected data from three: Clark – 16,500; New Town – 25,000; and Odessa – 51,000.
Estimate the populations of the remaining three cities, Grant, Lee and Lincoln, such that
the relation between the cities and their population is a function. How could this relation
not be a function?
For the relation to be a function each city must have a unique population; therefore, a
valid estimate would be Grant – 18,000, Lee – 19,000 and Lincoln -24,500. For the
relation not to be function one of the cities would need to have two population
estimates of different value. For example; Grant – 18,000 and Grant – 19,000.
2. For each of the following, add three values so that the relation will be a function and
three values so that the relation will not be a function.
A.
B.
C.
D.
{(1.2,__), (2.2, 1), (3,__), (-5, 0), (-2,2), (2, ___)}
{(1.2,__), (2.2, 1), (3,__), (-5, 0), (-2,2), (2, ___)}
Pearson Texas Algebra I
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name
2-6
Class
Date
Practice
Form G
Formalizing Relations and Functions
Identify the domain and range of each relation. Use a mapping diagram to determine
whether the relation is a function.
1. {(3, 6), (5, 7), (7, 7) (8, 9)}
2. {(0, 0.4), (1, 0.8), (2, 1.2), (3, 1.6)}
3. {(5, –4), (3, –5), (4, –3), (6, 4)}
4. {(0.3, 0.6), (0.4, 0.8), (0.3, 0.7), (0.5, 0.5)}
Use the vertical line test to determine whether the relation is a function.
5.
6.
7. Writing Explain when a relation is not a function.
8. How you can find the inverse of a function given the sets of the range and the domain?
9. Explain how the vertical line test can be used to determine if a relation is a
function.
Pearson Texas Algebra I
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name
2-6
Class
Date
Practice (continued)
Formalizing Relations and Functions
Plot each of the following functions, Use the vertical line test to determine whether the
relation is a function.
10. {(3, 6), (5, 7), (7, 7) (8, 9)}
11. {(0, 0.4), (1, 0.8), (2, 1.2), (3, 1.6)}
12. { (5, –4), (3, –5), (4, –3), (6, 4)}
13. {(0.3, 0.6), (0.4, 0.8), (0.3, 0.7), (0.5, 0.5)}
14. Reasoning Explain how a verbal description can be used to determine if
a relation is a function.
15. Describe the relationship between the relation, domain and range.
16. Given a table of points for 𝑥 and 𝑦, explain how to determine if the relation is a function.
Pearson Texas Algebra I
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Domain and Range Worksheet #1
Name: ____________________
State the domain and range for each graph and then tell if the graph is a function (write yes or no).
1) Domain
Range
Function?
2) Domain
Range
Function?
3) Domain
Range
Function?
4) Domain
Range
Function?
5) Domain
Range
Function?
6) Domain
Range
Function?
7) Domain
Range
Function?
8) Domain
Range
Function?
9) Domain
Range
Function?
10) Domain
Range
Function?
11) Domain
Range
Function?
12) Domain
Range
Function?
Draw a graph with the following domain and range. Identify whether the relation is a function and whether it is
continuous or discrete (circle one).
12) Domain: {-2, 0, 4}
Range: {-3, -1, 2, 3, 4}
Function? ___________
Continuous or Discrete?
15) Domain: all real numbers
Range: all real numbers
Function? ___________
Continuous or Discrete?
18) Domain: -5 ≤ x ≤ 7
Range: 0 ≤ y ≤ 3
Function? ___________
Continuous or Discrete?
13) Domain: 0 ≤ x ≤ 7
Range: -4 ≤ y ≤ 6
Function? ___________
Continuous or Discrete?
16) Domain: {1}
Range: {-1, 3, 6}
Function? ___________
Continuous or Discrete?
19) Domain: all real numbers
Range: 0 ≤ y ≤ ∞
Function? ___________
Continuous or Discrete?
14) Domain: -8 ≤ x ≤ 3
Range: -1 ≤ y ≤ 5
Function? ___________
Continuous or Discrete?
17) Domain: {-9, -6, -5, 0, 3, 4}
Range: {-2}
Function? ___________
Continuous or Discrete?
20) Domain: -∞ ≤ x ≤ 4
Range: all real numbers
Function? ___________
Continuous or Discrete?