High School

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 problem of understanding what [tex]$C(F)$[/tex] represents, let's break down the function and what it does:

1. Understanding the Function:
The function provided is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].

2. Purpose of the Function [tex]\( C(F) \)[/tex]:
This function is used to convert a temperature from degrees Fahrenheit to degrees Celsius.

3. Input and Output:
- Input [tex]\( F \)[/tex]: The input [tex]\( F \)[/tex] is the temperature in degrees Fahrenheit.
- Output [tex]\( C(F) \)[/tex]: The output [tex]\( C(F) \)[/tex] is the temperature in degrees Celsius.

4. Interpreting [tex]\( C(F) \)[/tex]:
Therefore, [tex]\( C(F) \)[/tex] represents the result or output value of this conversion function. The result is in degrees Celsius, and it translates the input, which was in degrees Fahrenheit, into degrees Celsius.

Based on this analysis, 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.

So, the correct choice 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.