Answer :
Certainly! Let's take a look at what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is telling us and what the question is asking.
The function [tex]\( C(F) \)[/tex] is used to convert temperatures from Fahrenheit to Celsius. Here's a step-by-step explanation:
1. Understand the Components of the Function:
- [tex]\( C \)[/tex] represents the function that gives the temperature in degrees Celsius.
- [tex]\( F \)[/tex] is the input of the function and represents the temperature in degrees Fahrenheit.
2. Interpret the Function:
- The expression [tex]\((F - 32)\)[/tex] is the first step in converting Fahrenheit to Celsius, where you subtract 32 from the Fahrenheit temperature.
- The fraction [tex]\(\frac{5}{9}\)[/tex] is then multiplied by [tex]\((F - 32)\)[/tex] to complete the conversion.
3. Determine What [tex]\( C(F) \)[/tex] Represents:
- With this function, you input a Fahrenheit temperature ([tex]\(F\)[/tex]) and the output will be the equivalent temperature in Celsius.
- Therefore, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius when the input is given in degrees Fahrenheit.
4. Select the Correct Explanation:
- Based on the function and what it represents, the correct interpretation 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."
This understanding helps to correctly interpret the conversion function and answer similar questions about temperature conversion using this formula.
The function [tex]\( C(F) \)[/tex] is used to convert temperatures from Fahrenheit to Celsius. Here's a step-by-step explanation:
1. Understand the Components of the Function:
- [tex]\( C \)[/tex] represents the function that gives the temperature in degrees Celsius.
- [tex]\( F \)[/tex] is the input of the function and represents the temperature in degrees Fahrenheit.
2. Interpret the Function:
- The expression [tex]\((F - 32)\)[/tex] is the first step in converting Fahrenheit to Celsius, where you subtract 32 from the Fahrenheit temperature.
- The fraction [tex]\(\frac{5}{9}\)[/tex] is then multiplied by [tex]\((F - 32)\)[/tex] to complete the conversion.
3. Determine What [tex]\( C(F) \)[/tex] Represents:
- With this function, you input a Fahrenheit temperature ([tex]\(F\)[/tex]) and the output will be the equivalent temperature in Celsius.
- Therefore, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius when the input is given in degrees Fahrenheit.
4. Select the Correct Explanation:
- Based on the function and what it represents, the correct interpretation 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."
This understanding helps to correctly interpret the conversion function and answer similar questions about temperature conversion using this formula.