Answer :
To solve the given problem, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents. This function is used to convert temperatures from degrees Fahrenheit to degrees Celsius.
Let's break down the function and process:
1. Understanding Celsius and Fahrenheit:
- Temperature can be measured in both Celsius (°C) and Fahrenheit (°F).
- In many places around the world, Celsius is commonly used, while Fahrenheit is more common in the United States.
2. Function Breakdown:
- The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a formula specifically designed to convert a temperature given in Fahrenheit (F) into Celsius (C).
- Here, [tex]\( F \)[/tex] is the input to the function, which represents the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output of the function, which gives the equivalent temperature in degrees Celsius.
3. Explanation of Conversion Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] works by first subtracting 32 from the Fahrenheit temperature. This adjusts the Fahrenheit scale to match the starting point of Celsius.
- Then, multiplying by [tex]\( \frac{5}{9} \)[/tex] converts the adjusted temperature to the Celsius scale because for every 9 degrees Fahrenheit, there are 5 degrees Celsius.
So, the function [tex]\( C(F) \)[/tex] takes the input temperature in degrees Fahrenheit and provides the output temperature in degrees Celsius, representing the conversion between these two temperature scales.
Therefore, the correct statement is:
"C(F) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit."
Let's break down the function and process:
1. Understanding Celsius and Fahrenheit:
- Temperature can be measured in both Celsius (°C) and Fahrenheit (°F).
- In many places around the world, Celsius is commonly used, while Fahrenheit is more common in the United States.
2. Function Breakdown:
- The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a formula specifically designed to convert a temperature given in Fahrenheit (F) into Celsius (C).
- Here, [tex]\( F \)[/tex] is the input to the function, which represents the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output of the function, which gives the equivalent temperature in degrees Celsius.
3. Explanation of Conversion Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] works by first subtracting 32 from the Fahrenheit temperature. This adjusts the Fahrenheit scale to match the starting point of Celsius.
- Then, multiplying by [tex]\( \frac{5}{9} \)[/tex] converts the adjusted temperature to the Celsius scale because for every 9 degrees Fahrenheit, there are 5 degrees Celsius.
So, the function [tex]\( C(F) \)[/tex] takes the input temperature in degrees Fahrenheit and provides the output temperature in degrees Celsius, representing the conversion between these two temperature scales.
Therefore, the correct statement is:
"C(F) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit."