Lesson 1-1

Example 1
OCEANOGRAPHY The table below shows the pounds per square inch (psi) of pressure that push on a body at various water depths. State the relation of the data as a set of ordered pairs. Also, state the domain and range of the relation.

Water Pressure
Depth (ft)
Pressure (psi)
0
14.7
16.5
22.05
33
29.4
49.5
36.75
66
44.1
82.5
51.45
99
58.8
115.5
66.15

Relation: {(0, 14.7), (16.5, 22.05), (33, 29.4), (49.5, 36.75), (66, 44.1), (82.5, 51.45),
(99, 58.8), (115.5, 66.15)}
Domain: {(0, 16.5, 33, 49.5, 66, 82.5, 99, 115.5}
Range: {14.7, 22.05, 29.4, 36.75, 44.1, 51.45, 58.8, 66.15}

Example 2
The domain of a relation is consecutive even integers between and including -4 and 4. The range, y, of the relation is three more than half x, where x is a member of the domain. Write the relation as a table of values and as an equation. Then graph the relation.

Table: x y

Graph:

-4
1

-2
2

0
3

2
4

4
5

Equation: Example 3
State the domain and range of each relation.

a.

b.

It appears from the graph that all real numbers are included in the domain and the range.
It appears from the graph that all real numbers are included in the Domain. The range includes all negative numbers and zero.

Example 4
State the domain and range of each relation. Then state whether the relation is a function.

a. {(-1, 2), (0, 4), (1, 3)}
The domain is {-1, 0, 1} and the range is {2, 3, 4}. Each element of the domain is paired with exactly one element of the range, so this relation is a function.

b. {(-3, 1), (-2, 5), (-3, 4), (1, 2)}
The domain is {-3, -2, -1} and the range is {1, 2, 4, 5}. In the domain, -3 is paired with two elements of the range, 1 and 4. Therefore, the relation is not a function.

Example 5
Determine if the graph of each relation represents a function. Explain.

a.

b.

No, the graph does not represent a function. Values of x > 0 are paired