Algebra I Lesson 10
Number Relations (Grades 9-12)

Pre-Test
Q&A	Introduction to Linear Relations

Instruction 10-2

Ordered Pairs |Relations | Equations as Relations | Graphing Linear Relations | Summary

RELATIONS 
CACS Algebra 16.0

A group of ordered pairs in the form of a set is called a relation. For example, all the sets below are relations.

S = {(–3, 5), (6, 21), (63, –12), (0, 0), (21, –21)}

T = {(0, –21), (21, 0), (–92, 89), (–32, 75), (4, 5)}

U = {(a, b), (–a, c), (–d, c), (–b, –a)}

The set of all the first elements of the pairs of a relation is called the domain of the relation. The domains of S, T, and U are as below.

Domain of S = {–3, 6, 63, 0, 21}

Domain of T = {0, 21, –92, –32, 4}

Domain of U = {a, –a, –d, –b}

The set of all the second elements of the pairs of a relation is called its range. The ranges of the above relations are as follows.

Range of S = {5, 21, –12, 0, –21}

Range of T = {–21, 0, 89, 75, 5}

Range of U = { c, –a}

Notice that you only list the elements of either the domain or the range ONCE, regardless of how many times they appear.

 
Practice 3
Determine domain and range of each relation.

D = {(a, ab), (–a, cd), (d, ad)}
E = {(–11, b), (–3, m), (m, –21), (a, 21)}
F = {3, 2a), (2a, –3), (–3, 4a), (5, –4a)}

Solution

Domain of D = {a, –a, d}
Range of D = {ab, cd, ad}
Domain of E = {–11, –3, m, a}
Range of E = {b, m, –21, 21}
Domain of F = {3, 2a, –3, 5}
Range of F = {2a, –3, 4a, –4a}
 
 
Practice 4
Write a relation whose domain and range are {1, 2, 3} and {5, 6, 7}, respectively.
 
Solution
{(1, 5), (1, 6), (1, 7), (2, 5), (2, 6), (2, 7), (3, 5), (3, 6), (3, 7)}

Another solution could be: {(1,5), (2,6),(3.7)}

A third solution could be: {(2,7),(1,6),(3.5)}

As you can see, there are many solutions to this particular problem, and all of them are correct.
 
 
 
Practice 5
The coordinates of points A, B, C, and D form a relation called S (Figure 10.6). Find the domain and the range of S.

 

Figure 10.6

Domain of S = {–4, –1, –2, 6}

Range of S = {–4, –3, 2, 4}

In which relation are the domain and the range are the same?

   A = {(–2, 2), (3, –3), (4, –4)}

B = {(5, 5), (6, 6), (1, 1)}

C = {(3, 6), (6, 3), (5, –6)}

         D = {(1, 2), (2, 3), (3, 4), (4, 1)}

In relations B and D

Find the domain and range of each relation.

K = {(a, a + b), (c, c + d), (a – b, a)}

L = (–2, m), (m, 2), (n, 3), (3, n)}

M = {(x, 2y), (3x, 6y), (–x, –2y), (0, 0)}

N = {(5, 5a), (6, 12a), (7a, 14a)}

Answer

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