Answer :
To determine what the function [tex]\( C(F) \)[/tex] represents, we need to understand its context and mathematical purpose. The function provided is:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
This equation is used to convert temperatures from degrees Fahrenheit ([tex]\( F \)[/tex]) to degrees Celsius ([tex]\( C \)[/tex]). Let's break down the options provided in the question:
1. Option 1: [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.
2. Option 2: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Fahrenheit when the input [tex]\( C \)[/tex] is in degrees Celsius.
3. Option 3: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Fahrenheit when the input [tex]\( F \)[/tex] is in degrees Celsius.
4. Option 4: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Celsius when the input [tex]\( C \)[/tex] is in degrees Fahrenheit.
To make sense of these:
- Option 1 correctly describes the function's purpose. The function [tex]\( C(F) \)[/tex] converts a temperature from Fahrenheit to Celsius. The output [tex]\( C(F) \)[/tex] is in degrees Celsius, and the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
- Option 2 is incorrect because it mistakenly swaps the roles of [tex]\( F \)[/tex] and [tex]\( C \)[/tex].
- Option 3 is incorrect because it suggests the output is in Fahrenheit, which goes against the function's conversion goal.
- Option 4 incorrectly swaps the roles and mistakenly suggests invert transformation.
Therefore, the correct option is Option 1: [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.
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
This equation is used to convert temperatures from degrees Fahrenheit ([tex]\( F \)[/tex]) to degrees Celsius ([tex]\( C \)[/tex]). Let's break down the options provided in the question:
1. Option 1: [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.
2. Option 2: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Fahrenheit when the input [tex]\( C \)[/tex] is in degrees Celsius.
3. Option 3: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Fahrenheit when the input [tex]\( F \)[/tex] is in degrees Celsius.
4. Option 4: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Celsius when the input [tex]\( C \)[/tex] is in degrees Fahrenheit.
To make sense of these:
- Option 1 correctly describes the function's purpose. The function [tex]\( C(F) \)[/tex] converts a temperature from Fahrenheit to Celsius. The output [tex]\( C(F) \)[/tex] is in degrees Celsius, and the input [tex]\( F \)[/tex] is in degrees Fahrenheit.
- Option 2 is incorrect because it mistakenly swaps the roles of [tex]\( F \)[/tex] and [tex]\( C \)[/tex].
- Option 3 is incorrect because it suggests the output is in Fahrenheit, which goes against the function's conversion goal.
- Option 4 incorrectly swaps the roles and mistakenly suggests invert transformation.
Therefore, the correct option is Option 1: [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.