To solve this problem, we need to identify the domain and range of the function [tex]\( f(x) \)[/tex], which is given as a set of ordered pairs:
[tex]\[ f(x) = \{ (-25, 80), (-24, 97), (-16, 12), (3, 64), (7, 1), (25, 30) \} \][/tex]
### Domain
The domain of a function is the set of all possible input values (x-values) from the ordered pairs. We will extract the x-values from each ordered pair:
- For [tex]\((-25, 80)\)[/tex], the x-value is [tex]\(-25\)[/tex]
- For [tex]\((-24, 97)\)[/tex], the x-value is [tex]\(-24\)[/tex]
- For [tex]\((-16, 12)\)[/tex], the x-value is [tex]\(-16\)[/tex]
- For [tex]\((3, 64)\)[/tex], the x-value is [tex]\(3\)[/tex]
- For [tex]\((7, 1)\)[/tex], the x-value is [tex]\(7\)[/tex]
- For [tex]\((25, 30)\)[/tex], the x-value is [tex]\(25\)[/tex]
Next, we list these values in ascending order:
[tex]\[
\{ -25, -24, -16, 3, 7, 25 \}
\][/tex]
Thus, the domain of [tex]\( f(x) \)[/tex] is:
[tex]\[
\{ -25, -24, -16, 3, 7, 25 \}
\][/tex]
### Range
The range of a function is the set of all possible output values (y-values) from the ordered pairs. We will extract the y-values from each ordered pair:
- For [tex]\((-25, 80)\)[/tex], the y-value is [tex]\(80\)[/tex]
- For [tex]\((-24, 97)\)[/tex], the y-value is [tex]\(97\)[/tex]
- For [tex]\((-16, 12)\)[/tex], the y-value is [tex]\(12\)[/tex]
- For [tex]\((3, 64)\)[/tex], the y-value is [tex]\(64\)[/tex]
- For [tex]\((7, 1)\)[/tex], the y-value is [tex]\(1\)[/tex]
- For [tex]\((25, 30)\)[/tex], the y-value is [tex]\(30\)[/tex]
Next, we list these values in ascending order:
[tex]\[
\{ 1, 12, 30, 64, 80, 97 \}
\][/tex]
Thus, the range of [tex]\( f(x) \)[/tex] is:
[tex]\[
\{ 1, 12, 30, 64, 80, 97 \}
\][/tex]
### Final Answer
[tex]\[
\text{Domain:} \{ -25, -24, -16, 3, 7, 25 \}
\][/tex]
[tex]\[
\text{Range:} \{ 1, 12, 30, 64, 80, 97 \}
\][/tex]
