Answer :
To solve this question, let's break down what we are trying to understand and what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] does:
1. Understanding the Function: The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert temperatures from Fahrenheit to Celsius.
2. Function Notation: Here, [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit, and [tex]\( C(F) \)[/tex] is the result of converting that Fahrenheit temperature to degrees Celsius.
3. Conversion Explanation:
- Start with a temperature in Fahrenheit [tex]\( F \)[/tex].
- Subtract 32 from [tex]\( F \)[/tex]. This accounts for the difference in the starting points of the Fahrenheit and Celsius scales (since water freezes at 32°F and 0°C).
- Multiply the result by [tex]\(\frac{5}{9}\)[/tex]. This accounts for the different scale gradients (Fahrenheit has more degrees over the same temperature range compared to Celsius; specifically, every increase of 1 degree Celsius corresponds to an increase of [tex]\( \frac{9}{5} \)[/tex] degrees Fahrenheit).
4. Conclusion: After performing these operations, [tex]\( C(F) \)[/tex] gives us the converted temperature in degrees Celsius.
Based on this explanation, [tex]\( C(F) \)[/tex] represents the temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius. So the correct answer is:
The temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius.
1. Understanding the Function: The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert temperatures from Fahrenheit to Celsius.
2. Function Notation: Here, [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit, and [tex]\( C(F) \)[/tex] is the result of converting that Fahrenheit temperature to degrees Celsius.
3. Conversion Explanation:
- Start with a temperature in Fahrenheit [tex]\( F \)[/tex].
- Subtract 32 from [tex]\( F \)[/tex]. This accounts for the difference in the starting points of the Fahrenheit and Celsius scales (since water freezes at 32°F and 0°C).
- Multiply the result by [tex]\(\frac{5}{9}\)[/tex]. This accounts for the different scale gradients (Fahrenheit has more degrees over the same temperature range compared to Celsius; specifically, every increase of 1 degree Celsius corresponds to an increase of [tex]\( \frac{9}{5} \)[/tex] degrees Fahrenheit).
4. Conclusion: After performing these operations, [tex]\( C(F) \)[/tex] gives us the converted temperature in degrees Celsius.
Based on this explanation, [tex]\( C(F) \)[/tex] represents the temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius. So the correct answer is:
The temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius.