Answer :
To understand what [tex]$C(F)$[/tex] represents, let's break down the function presented:
The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert temperatures from degrees Fahrenheit (F) to degrees Celsius (C). Let’s see what each part means:
1. Function Definition: [tex]\( C(F) \)[/tex] is a function where [tex]\( F \)[/tex] is the input, representing a temperature in degrees Fahrenheit.
2. Calculation:
- Inside the function, we have [tex]\( (F - 32) \)[/tex], which is the first step in converting Fahrenheit to Celsius.
- Multiplying by [tex]\( \frac{5}{9} \)[/tex] completes the conversion from Fahrenheit to Celsius.
3. Output:
- The result of the calculation, [tex]\( C(F) \)[/tex], gives us the temperature in degrees Celsius.
Now, let's look at the options provided:
- 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".
- This option correctly describes the process of converting a Fahrenheit temperature to Celsius using the function [tex]\( C(F) \)[/tex].
- 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".
- This is incorrect since it reverses the roles of [tex]\( C \)[/tex] and [tex]\( F \)[/tex].
- 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".
- This is incorrect because the output should be in degrees Celsius, and the input is supposed to be in degrees Fahrenheit.
- 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".
- This statement is incorrect because it misrepresents the input and output relationship.
Therefore, the correct choice 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".
The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert temperatures from degrees Fahrenheit (F) to degrees Celsius (C). Let’s see what each part means:
1. Function Definition: [tex]\( C(F) \)[/tex] is a function where [tex]\( F \)[/tex] is the input, representing a temperature in degrees Fahrenheit.
2. Calculation:
- Inside the function, we have [tex]\( (F - 32) \)[/tex], which is the first step in converting Fahrenheit to Celsius.
- Multiplying by [tex]\( \frac{5}{9} \)[/tex] completes the conversion from Fahrenheit to Celsius.
3. Output:
- The result of the calculation, [tex]\( C(F) \)[/tex], gives us the temperature in degrees Celsius.
Now, let's look at the options provided:
- 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".
- This option correctly describes the process of converting a Fahrenheit temperature to Celsius using the function [tex]\( C(F) \)[/tex].
- 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".
- This is incorrect since it reverses the roles of [tex]\( C \)[/tex] and [tex]\( F \)[/tex].
- 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".
- This is incorrect because the output should be in degrees Celsius, and the input is supposed to be in degrees Fahrenheit.
- 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".
- This statement is incorrect because it misrepresents the input and output relationship.
Therefore, the correct choice 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".