Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
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]
[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]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.