Answer :
To solve this problem, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is doing. The function is used to convert temperatures from degrees Fahrenheit to degrees Celsius. Let’s break it down step by step:
1. Identify and Define the Function:
- The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
- Here, [tex]\( F \)[/tex] represents the input temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output, which gives us the temperature in degrees Celsius.
2. Understanding the Conversion Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a standard formula used for converting Fahrenheit to Celsius.
- The part [tex]\((F - 32)\)[/tex] adjusts the Fahrenheit temperature by subtracting 32, which is necessary because 32°F corresponds to 0°C.
- Multiplying by [tex]\(\frac{5}{9}\)[/tex] scales the adjusted Fahrenheit temperature to its equivalent in Celsius.
3. Interpret the Function:
- Based on the structure of the function, [tex]\( C(F) \)[/tex] represents the converted temperature in degrees Celsius.
- Thus, [tex]\( C(F) \)[/tex] is the Celsius equivalent of the given temperature [tex]\( F \)[/tex] in degrees Fahrenheit.
4. Choose the Correct Representation:
- The correct interpretation is that [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
Therefore, the correct answer is:
"[tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit."
1. Identify and Define the Function:
- The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
- Here, [tex]\( F \)[/tex] represents the input temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output, which gives us the temperature in degrees Celsius.
2. Understanding the Conversion Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a standard formula used for converting Fahrenheit to Celsius.
- The part [tex]\((F - 32)\)[/tex] adjusts the Fahrenheit temperature by subtracting 32, which is necessary because 32°F corresponds to 0°C.
- Multiplying by [tex]\(\frac{5}{9}\)[/tex] scales the adjusted Fahrenheit temperature to its equivalent in Celsius.
3. Interpret the Function:
- Based on the structure of the function, [tex]\( C(F) \)[/tex] represents the converted temperature in degrees Celsius.
- Thus, [tex]\( C(F) \)[/tex] is the Celsius equivalent of the given temperature [tex]\( F \)[/tex] in degrees Fahrenheit.
4. Choose the Correct Representation:
- The correct interpretation is that [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
Therefore, the correct answer is:
"[tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit."