Answer :
Sure, let's work through what the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] means step by step.
1. Understanding the Function: The function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] is used to convert temperatures from degrees Fahrenheit to degrees Celsius. Here, [tex]\( F \)[/tex] represents the temperature in Fahrenheit, and [tex]\( C(F) \)[/tex] will give us the temperature in Celsius.
2. Converting Fahrenheit to Celsius: The formula [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] works by first subtracting 32 from the Fahrenheit temperature. This adjusts for the differences in the Fahrenheit scale. Then, the result is multiplied by [tex]\(\frac{5}{9}\)[/tex] to convert the remaining temperature from Fahrenheit to Celsius.
3. Identifying the Components:
- [tex]\( F \)[/tex]: This is the input into the function and represents the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex]: This is the output from the function that provides the temperature in degrees Celsius.
4. What Does [tex]\( C(F) \)[/tex] Represent?: Based on the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex], we can say:
- [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
This step-by-step breakdown shows that the correct interpretation of [tex]\( C(F) \)[/tex] is that it provides the temperature in Celsius for a given temperature in Fahrenheit using the provided conversion formula.
1. Understanding the Function: The function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] is used to convert temperatures from degrees Fahrenheit to degrees Celsius. Here, [tex]\( F \)[/tex] represents the temperature in Fahrenheit, and [tex]\( C(F) \)[/tex] will give us the temperature in Celsius.
2. Converting Fahrenheit to Celsius: The formula [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] works by first subtracting 32 from the Fahrenheit temperature. This adjusts for the differences in the Fahrenheit scale. Then, the result is multiplied by [tex]\(\frac{5}{9}\)[/tex] to convert the remaining temperature from Fahrenheit to Celsius.
3. Identifying the Components:
- [tex]\( F \)[/tex]: This is the input into the function and represents the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex]: This is the output from the function that provides the temperature in degrees Celsius.
4. What Does [tex]\( C(F) \)[/tex] Represent?: Based on the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex], we can say:
- [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
This step-by-step breakdown shows that the correct interpretation of [tex]\( C(F) \)[/tex] is that it provides the temperature in Celsius for a given temperature in Fahrenheit using the provided conversion formula.