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, we need to look at the function provided:

[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]

This function is used to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C). Let's break down the process:

1. Identify what [tex]\( F \)[/tex] represents:
- [tex]\( F \)[/tex] stands for the temperature in degrees Fahrenheit that you want to convert to Celsius.

2. Understand the conversion formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is the mathematical expression used to convert Fahrenheit to Celsius.
- First, you subtract 32 from the Fahrenheit temperature. This is part of the conversion formula because 32 is the freezing point of water in Fahrenheit, while 0 is the freezing point in Celsius.
- Then, you multiply the result by [tex]\( \frac{5}{9} \)[/tex]. This fraction adjusts for the different sizes of the Fahrenheit and Celsius degrees.

3. Determine what [tex]\( C(F) \)[/tex] represents:
- [tex]\( C(F) \)[/tex] is the output of this function. After applying the formula, [tex]\( C(F) \)[/tex] gives you the temperature in degrees Celsius.
- Essentially, [tex]\( C(F) \)[/tex] represents the converted temperature value in Celsius when the input temperature is in Fahrenheit.

Therefore, [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.