College

For one month, Siera calculated her hometown's average high temperature in degrees Fahrenheit. She wants to convert that temperature from degrees Fahrenheit to degrees Celsius using the function [tex]C(F) = \frac{5}{9}(F - 32)[/tex].

What does [tex]C(F)[/tex] represent?

A. [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.

B. [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.

C. [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.

D. [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.

Answer :

To solve the given problem, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents:

1. Identify the Purpose of the Function:
- The function [tex]\( C(F) \)[/tex] is used to convert a temperature value from degrees Fahrenheit (indicated by [tex]\( F \)[/tex]) to degrees Celsius.

2. Understanding the Notation:
- [tex]\( C(F) \)[/tex] indicates that the function uses [tex]\( F \)[/tex] (a temperature given in Fahrenheit) as an input and produces an output.
- The formula involves subtracting 32 from the Fahrenheit temperature and then multiplying the result by [tex]\(\frac{5}{9}\)[/tex], which is the standard formula to convert Fahrenheit to Celsius.

3. Analyze the Answer Choices:
- Choice 1: "C(F) represents the output of the function C in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit."
- This describes exactly what the function does: it converts temperatures from Fahrenheit to Celsius.

- Choice 2: "C(F) 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 because it reverses the roles of the variables and the conversion direction.

- Choice 3: "C(F) represents the output of the function [tex]\( C \)[/tex] in degrees Fahrenheit when the input [tex]\( F \)[/tex] is in degrees Gelsius."
- This contains a typo and also suggests the wrong temperature conversion direction.

- Choice 4: "C(F) represents the output of the function [tex]\( F \)[/tex] in degrees Celsius when the input [tex]\( C \)[/tex] is in degrees Fahrenheit."
- This option confuses the roles of the inputs and outputs; it does not describe the conversion correctly.

4. Conclusion:
- Based on the definitions and purpose of the function, the correct choice is the first one: "C(F) represents the output of the function C in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit."

This is the correct interpretation of what [tex]\( C(F) \)[/tex] represents, as it aligns with the function’s role in converting a Fahrenheit temperature to Celsius.