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 understand what [tex]\( C(F) \)[/tex] represents, let's break down the given function and choices:

We have the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This is a formula used to convert temperatures from degrees Fahrenheit ([tex]\( F \)[/tex]) to degrees Celsius ([tex]\( C \)[/tex]).

1. Understand the Function:
- The function takes an input [tex]\( F \)[/tex], which stands for the temperature in degrees Fahrenheit.
- It outputs [tex]\( C(F) \)[/tex], which is the temperature converted to degrees Celsius.

Given this function, let's evaluate the choices:

- Choice 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 choice matches exactly what the function does: it converts [tex]\( F \)[/tex] (Fahrenheit) into [tex]\( C(F) \)[/tex] (Celsius).

- Choice 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 because it reverses the roles of Fahrenheit and Celsius.

- Choice 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. The function is not converting to Fahrenheit; it converts from Fahrenheit to Celsius.

- Choice 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 is a confused statement as [tex]\( C(F) \)[/tex] is not an input-output pair between these variables in this way.

Therefore, the correct choice is Choice 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.