Answer :
To understand what [tex]\( C(F) \)[/tex] represents in the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex], let’s go through the steps to convert a temperature from Fahrenheit to Celsius.
### Step-by-Step Explanation:
1. Formula Understanding:
- The given function is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
- This function is used for converting temperatures from Fahrenheit to Celsius.
2. Breaking Down the Formula:
- In the formula, [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- The expression [tex]\( (F - 32) \)[/tex] adjusts the Fahrenheit temperature by subtracting 32 because the freezing point of water is 32°F.
- The factor [tex]\( \frac{5}{9} \)[/tex] is used to convert the adjusted temperature difference from the Fahrenheit scale to the Celsius scale.
3. Conversion Process:
- When you input a temperature in Fahrenheit (denoted as [tex]\( F \)[/tex]) into the function [tex]\( C(F) \)[/tex], the function first subtracts 32 from [tex]\( F \)[/tex].
- Then, it multiplies the result by [tex]\( \frac{5}{9} \)[/tex], converting the temperature from Fahrenheit units to Celsius units.
4. Meaning of [tex]\( C(F) \)[/tex]:
- [tex]\( C(F) \)[/tex] provides the corresponding temperature in degrees Celsius after converting from the given temperature in degrees Fahrenheit.
### Conclusion:
Given this understanding, the correct interpretation of [tex]\( C(F) \)[/tex] is:
- [tex]\( C(F) \)[/tex] represents the temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius.
This tells us that when we input a temperature in degrees Fahrenheit into the function, the output is the equivalent temperature in degrees Celsius.
### Step-by-Step Explanation:
1. Formula Understanding:
- The given function is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
- This function is used for converting temperatures from Fahrenheit to Celsius.
2. Breaking Down the Formula:
- In the formula, [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- The expression [tex]\( (F - 32) \)[/tex] adjusts the Fahrenheit temperature by subtracting 32 because the freezing point of water is 32°F.
- The factor [tex]\( \frac{5}{9} \)[/tex] is used to convert the adjusted temperature difference from the Fahrenheit scale to the Celsius scale.
3. Conversion Process:
- When you input a temperature in Fahrenheit (denoted as [tex]\( F \)[/tex]) into the function [tex]\( C(F) \)[/tex], the function first subtracts 32 from [tex]\( F \)[/tex].
- Then, it multiplies the result by [tex]\( \frac{5}{9} \)[/tex], converting the temperature from Fahrenheit units to Celsius units.
4. Meaning of [tex]\( C(F) \)[/tex]:
- [tex]\( C(F) \)[/tex] provides the corresponding temperature in degrees Celsius after converting from the given temperature in degrees Fahrenheit.
### Conclusion:
Given this understanding, the correct interpretation of [tex]\( C(F) \)[/tex] is:
- [tex]\( C(F) \)[/tex] represents the temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius.
This tells us that when we input a temperature in degrees Fahrenheit into the function, the output is the equivalent temperature in degrees Celsius.
