Answer :
To solve this problem, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] represents. The function is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
Here's a breakdown of what each part represents:
1. Function Name and Notation:
- [tex]\( C(F) \)[/tex] is the notation used for the function. This means [tex]\( C \)[/tex] is the function name, and [tex]\( F \)[/tex] is the input to the function, which stands for the temperature in degrees Fahrenheit.
2. Mathematical Conversion:
- The formula [tex]\( \frac{5}{9}(F-32) \)[/tex] is the standard conversion formula used to convert a temperature from Fahrenheit to Celsius.
- In this formula:
- [tex]\( F \)[/tex] is the temperature in Fahrenheit.
- [tex]\( F - 32 \)[/tex] adjusts for the fact that 32°F is the freezing point of water in Fahrenheit.
- The fraction [tex]\( \frac{5}{9} \)[/tex] is a constant used to scale the result to Celsius.
3. Output Interpretation:
- The result [tex]\( C(F) \)[/tex] gives us the temperature in degrees Celsius after the conversion.
Based on this understanding, the correct interpretation of 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.
This option correctly describes the purpose and output of the function.
Here's a breakdown of what each part represents:
1. Function Name and Notation:
- [tex]\( C(F) \)[/tex] is the notation used for the function. This means [tex]\( C \)[/tex] is the function name, and [tex]\( F \)[/tex] is the input to the function, which stands for the temperature in degrees Fahrenheit.
2. Mathematical Conversion:
- The formula [tex]\( \frac{5}{9}(F-32) \)[/tex] is the standard conversion formula used to convert a temperature from Fahrenheit to Celsius.
- In this formula:
- [tex]\( F \)[/tex] is the temperature in Fahrenheit.
- [tex]\( F - 32 \)[/tex] adjusts for the fact that 32°F is the freezing point of water in Fahrenheit.
- The fraction [tex]\( \frac{5}{9} \)[/tex] is a constant used to scale the result to Celsius.
3. Output Interpretation:
- The result [tex]\( C(F) \)[/tex] gives us the temperature in degrees Celsius after the conversion.
Based on this understanding, the correct interpretation of 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.
This option correctly describes the purpose and output of the function.