Answer :
To find what [tex]\( C(F) \)[/tex] represents, we need to understand the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex].
1. Function Overview: The function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] is used to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C).
2. Understanding the Formula:
- [tex]\( F \)[/tex] is the input to the function, representing temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output of the function, which will be the equivalent temperature in degrees Celsius.
3. Conversion Explanation:
- The formula subtracts 32 from the Fahrenheit temperature because 32 degrees Fahrenheit is the freezing point of water, which corresponds to 0 degrees Celsius.
- It then multiplies the result by [tex]\(\frac{5}{9}\)[/tex] to convert the temperature from a Fahrenheit-based scale to a Celsius-based scale. This is because each degree Fahrenheit is equivalent to [tex]\(\frac{5}{9}\)[/tex] of a degree Celsius.
4. Terminology and Representation:
- Since [tex]\( C(F) \)[/tex] is the result when you input Fahrenheit into the function, and it gives you the temperature in Celsius, [tex]\( C(F) \)[/tex] represents the output in degrees Celsius for a given input in degrees Fahrenheit.
Therefore, the correct representation of [tex]\( C(F) \)[/tex] is:
"C(F) represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit."
1. Function Overview: The function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] is used to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C).
2. Understanding the Formula:
- [tex]\( F \)[/tex] is the input to the function, representing temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output of the function, which will be the equivalent temperature in degrees Celsius.
3. Conversion Explanation:
- The formula subtracts 32 from the Fahrenheit temperature because 32 degrees Fahrenheit is the freezing point of water, which corresponds to 0 degrees Celsius.
- It then multiplies the result by [tex]\(\frac{5}{9}\)[/tex] to convert the temperature from a Fahrenheit-based scale to a Celsius-based scale. This is because each degree Fahrenheit is equivalent to [tex]\(\frac{5}{9}\)[/tex] of a degree Celsius.
4. Terminology and Representation:
- Since [tex]\( C(F) \)[/tex] is the result when you input Fahrenheit into the function, and it gives you the temperature in Celsius, [tex]\( C(F) \)[/tex] represents the output in degrees Celsius for a given input in degrees Fahrenheit.
Therefore, the correct representation of [tex]\( C(F) \)[/tex] is:
"C(F) represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit."