Answer :
Certainly! Let's break this down step-by-step to understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents.
1. Identify the Function: The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a standard formula used to convert temperatures from degrees Fahrenheit to degrees Celsius.
2. Understanding Inputs and Outputs:
- Input (F): This is the temperature in degrees Fahrenheit—the value you start with.
- Output/C(F): This is what the function calculates and provides you with, which is the temperature in degrees Celsius.
3. Purpose of the Function: The entire purpose of this function is to take a temperature reading in Fahrenheit (input, [tex]\( F \)[/tex]) and convert it to Celsius (output, [tex]\( C(F) \)[/tex]).
4. Verifying What [tex]\( C(F) \)[/tex] Represents:
- The function name [tex]\( C \)[/tex] suggests it’s about Celsius because [tex]\( C \)[/tex] is commonly used to denote temperature in degrees Celsius.
- The expression inside the function takes an [tex]\( F \)[/tex] value (Fahrenheit) and converts it to Celsius.
5. Choose the Correct Interpretation:
- After analyzing the components and the form of the function, the correct choice is:
- [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.
Therefore, the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] indeed represents the conversion from Fahrenheit to Celsius, where [tex]\( C(F) \)[/tex] is the temperature in Celsius and [tex]\( F \)[/tex] is the temperature in Fahrenheit.
1. Identify the Function: The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a standard formula used to convert temperatures from degrees Fahrenheit to degrees Celsius.
2. Understanding Inputs and Outputs:
- Input (F): This is the temperature in degrees Fahrenheit—the value you start with.
- Output/C(F): This is what the function calculates and provides you with, which is the temperature in degrees Celsius.
3. Purpose of the Function: The entire purpose of this function is to take a temperature reading in Fahrenheit (input, [tex]\( F \)[/tex]) and convert it to Celsius (output, [tex]\( C(F) \)[/tex]).
4. Verifying What [tex]\( C(F) \)[/tex] Represents:
- The function name [tex]\( C \)[/tex] suggests it’s about Celsius because [tex]\( C \)[/tex] is commonly used to denote temperature in degrees Celsius.
- The expression inside the function takes an [tex]\( F \)[/tex] value (Fahrenheit) and converts it to Celsius.
5. Choose the Correct Interpretation:
- After analyzing the components and the form of the function, the correct choice is:
- [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.
Therefore, the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] indeed represents the conversion from Fahrenheit to Celsius, where [tex]\( C(F) \)[/tex] is the temperature in Celsius and [tex]\( F \)[/tex] is the temperature in Fahrenheit.