Answer :
To solve the problem of understanding what [tex]\( C(F) \)[/tex] represents in the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex], let's break it down:
1. Understanding the Function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex]:
- This function is used to convert temperatures from degrees Fahrenheit to degrees Celsius.
- The input [tex]\( F \)[/tex] represents a temperature in degrees Fahrenheit.
2. Conversion Process:
- The formula involves subtracting 32 from the Fahrenheit temperature, which is the first step in adjusting for the offset between the Fahrenheit and Celsius scales.
- Then, the result is multiplied by [tex]\(\frac{5}{9}\)[/tex]. This scales the difference to align with the Celsius scale, since the ratio of the degrees between the two scales is 9/5.
3. What [tex]\( C(F) \)[/tex] Represents:
- Given that the input [tex]\( F \)[/tex] is in degrees Fahrenheit, the function performs the conversion to give a temperature in degrees Celsius.
- Therefore, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius after converting from [tex]\( F \)[/tex] degrees Fahrenheit.
4. Conclusion:
- The correct interpretation of [tex]\( C(F) \)[/tex] is: "the temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius."
This aligns with the option that states: "the temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius."
1. Understanding the Function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex]:
- This function is used to convert temperatures from degrees Fahrenheit to degrees Celsius.
- The input [tex]\( F \)[/tex] represents a temperature in degrees Fahrenheit.
2. Conversion Process:
- The formula involves subtracting 32 from the Fahrenheit temperature, which is the first step in adjusting for the offset between the Fahrenheit and Celsius scales.
- Then, the result is multiplied by [tex]\(\frac{5}{9}\)[/tex]. This scales the difference to align with the Celsius scale, since the ratio of the degrees between the two scales is 9/5.
3. What [tex]\( C(F) \)[/tex] Represents:
- Given that the input [tex]\( F \)[/tex] is in degrees Fahrenheit, the function performs the conversion to give a temperature in degrees Celsius.
- Therefore, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius after converting from [tex]\( F \)[/tex] degrees Fahrenheit.
4. Conclusion:
- The correct interpretation of [tex]\( C(F) \)[/tex] is: "the temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius."
This aligns with the option that states: "the temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius."