Answer :
To understand what [tex]\( C(F) \)[/tex] represents in the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex], let's break down the details:
1. Understanding the Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert a temperature from degrees Fahrenheit ([tex]\( F \)[/tex]) to degrees Celsius ([tex]\( C \)[/tex]).
- It adjusts for the offset of the freezing point of water, which is 32 degrees Fahrenheit, and applies a conversion factor of [tex]\(\frac{5}{9}\)[/tex] to account for the difference in size of the Fahrenheit and Celsius degrees.
2. Identifying What [tex]\( C(F) \)[/tex] Represents:
- In the expression [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex], [tex]\( F \)[/tex] refers to the temperature in degrees Fahrenheit you want to convert.
- By substituting the Fahrenheit temperature ([tex]\( F \)[/tex]) into the formula, you apply the conversion process which outputs the corresponding temperature in degrees Celsius.
- Therefore, [tex]\( C(F) \)[/tex] represents the temperature that was originally measured in degrees Fahrenheit, now converted into degrees Celsius.
3. Conclusion:
- Based on this understanding, the correct interpretation is:
- The temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius.
This explanation clarifies that [tex]\( C(F) \)[/tex] is a function designed to take a Fahrenheit temperature and convert it into a Celsius temperature, using the given formula.
1. Understanding the Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert a temperature from degrees Fahrenheit ([tex]\( F \)[/tex]) to degrees Celsius ([tex]\( C \)[/tex]).
- It adjusts for the offset of the freezing point of water, which is 32 degrees Fahrenheit, and applies a conversion factor of [tex]\(\frac{5}{9}\)[/tex] to account for the difference in size of the Fahrenheit and Celsius degrees.
2. Identifying What [tex]\( C(F) \)[/tex] Represents:
- In the expression [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex], [tex]\( F \)[/tex] refers to the temperature in degrees Fahrenheit you want to convert.
- By substituting the Fahrenheit temperature ([tex]\( F \)[/tex]) into the formula, you apply the conversion process which outputs the corresponding temperature in degrees Celsius.
- Therefore, [tex]\( C(F) \)[/tex] represents the temperature that was originally measured in degrees Fahrenheit, now converted into degrees Celsius.
3. Conclusion:
- Based on this understanding, the correct interpretation is:
- The temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius.
This explanation clarifies that [tex]\( C(F) \)[/tex] is a function designed to take a Fahrenheit temperature and convert it into a Celsius temperature, using the given formula.