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 understand what [tex]$C(F)$[/tex] represents in the function given, let's break down the components:

1. Understanding the Function:
- The function provided is [tex]\( C(n) = \frac{5}{9}(F - 32) \)[/tex].
- This function is used to convert a temperature from degrees Fahrenheit to degrees Celsius.

2. Identifying the Variables:
- [tex]\( F \)[/tex] represents a temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] symbolizes the output of the function, which will be in degrees Celsius.

3. Evaluating the Options:
- 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 purpose of the function: to convert from Fahrenheit to Celsius.
- 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 option incorrectly reverses the conversion process.
- 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 option incorrectly states both the input and output units.
- 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 option incorrectly assigns the role of the functions and their corresponding inputs and outputs.

By evaluating these, we find that Option 1 is the correct description. [tex]$C(F)$[/tex] indeed represents the output of the function [tex]$C$[/tex] in degrees Celsius when the input [tex]$F$[/tex] is in degrees Fahrenheit.