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 in the given function, let’s break it down step by step.

1. Identify the Purpose of the Function:
The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This formula is used to convert temperatures from degrees Fahrenheit to degrees Celsius. It’s a standard formula known for its purpose of making temperature conversions between these two units.

2. Understand the Input and Output:
- The input of the function, denoted by [tex]\( F \)[/tex], represents the temperature in degrees Fahrenheit that you want to convert.
- The output of the function, which is [tex]\( C(F) \)[/tex], represents the converted temperature in degrees Celsius.

3. Interpret the Symbols:
- [tex]\( C(F) \)[/tex] is the function notation.
- Here, [tex]\( C \)[/tex] stands for Celsius, and [tex]\( F \)[/tex] stands for Fahrenheit. It helps us understand that C is calculated as a function of F.

4. Correct Interpretation of [tex]\( C(F) \)[/tex]:
- Since [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] converts a Fahrenheit temperature to Celsius, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius when the temperature in degrees Fahrenheit is used as the input.

So, the correct interpretation of the function [tex]\( C(F) \)[/tex] is:
"C(F) represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit."