Answer :
To understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents, let's break it down step by step:
1. Identify the Variables:
- [tex]\( C(F) \)[/tex] is the output of the function.
- [tex]\( F \)[/tex] is the input to the function, representing the temperature in degrees Fahrenheit.
2. Understand the Function:
- The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a standard formula used to convert temperatures from degrees Fahrenheit to degrees Celsius.
3. Analyze the Components:
- The part [tex]\( F - 32 \)[/tex] adjusts the input temperature in Fahrenheit by subtracting 32. This is because the freezing point of water is 32 degrees Fahrenheit, which corresponds to 0 degrees Celsius.
- Multiplying by [tex]\( \frac{5}{9} \)[/tex] is necessary to adjust the scale between Fahrenheit and Celsius, since each unit of Celsius is larger than a unit of Fahrenheit.
4. Determine What [tex]\( C(F) \)[/tex] Represents:
- [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius.
- It is the result we obtain after substituting a Fahrenheit temperature into the function and performing the conversion calculation.
5. Conclusion:
- Therefore, the correct interpretation of [tex]\( C(F) \)[/tex] is: it represents the output of the function in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
So, the option that correctly describes what [tex]\( C(F) \)[/tex] represents 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 the Variables:
- [tex]\( C(F) \)[/tex] is the output of the function.
- [tex]\( F \)[/tex] is the input to the function, representing the temperature in degrees Fahrenheit.
2. Understand the Function:
- The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a standard formula used to convert temperatures from degrees Fahrenheit to degrees Celsius.
3. Analyze the Components:
- The part [tex]\( F - 32 \)[/tex] adjusts the input temperature in Fahrenheit by subtracting 32. This is because the freezing point of water is 32 degrees Fahrenheit, which corresponds to 0 degrees Celsius.
- Multiplying by [tex]\( \frac{5}{9} \)[/tex] is necessary to adjust the scale between Fahrenheit and Celsius, since each unit of Celsius is larger than a unit of Fahrenheit.
4. Determine What [tex]\( C(F) \)[/tex] Represents:
- [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius.
- It is the result we obtain after substituting a Fahrenheit temperature into the function and performing the conversion calculation.
5. Conclusion:
- Therefore, the correct interpretation of [tex]\( C(F) \)[/tex] is: it represents the output of the function in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
So, the option that correctly describes what [tex]\( C(F) \)[/tex] represents 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.