The function

Question

f
(
x
)
is defined as a set or ordered pairs. Using that set of data, identify the Domain and Range of
f
(
x
)
.

Write your answer as an ordered list enclosed in curly brackets.
f
(
x
)
=
{
(
−
22
,
20
)
,

(
4
,
35
)
,

(
7
,
96
)
,

(
15
,
7
)
,

(
31
,
57
)
,

(
36
,
84
)
}

Domain:
Range:

Answer 1

To identify the domain and range of the function \( f(x) \) defined by the set of ordered pairs, we'll extract the first elements (inputs) for the domain and the second elements (outputs) for the range.

The given set of ordered pairs is:

\[ f(x) = { (-22, 20), (4, 35), (7, 96), (15, 7), (31, 57), (36, 84) } \]

Domain (the set of all first elements):

• From the pairs:
  • First element of (-22, 20) is -22
  • First element of (4, 35) is 4
  • First element of (7, 96) is 7
  • First element of (15, 7) is 15
  • First element of (31, 57) is 31
  • First element of (36, 84) is 36

So, the domain is:

\[ \text{Domain} = { -22, 4, 7, 15, 31, 36 } \]

Range (the set of all second elements):

• From the pairs:
  • Second element of (-22, 20) is 20
  • Second element of (4, 35) is 35
  • Second element of (7, 96) is 96
  • Second element of (15, 7) is 7
  • Second element of (31, 57) is 57
  • Second element of (36, 84) is 84

So, the range is:

\[ \text{Range} = { 20, 35, 96, 7, 57, 84 } \]

Putting it all together:

\[ \text{Domain: } { -22, 4, 7, 15, 31, 36 } \] \[ \text{Range: } { 20, 35, 96, 7, 57, 84 } \]