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 solve this problem, let's first understand the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This function is used to convert temperatures from degrees Fahrenheit to degrees Celsius.

Here's a detailed step-by-step explanation:

1. Understand the Function:
- [tex]\( C(F) \)[/tex] is a mathematical function that takes an input [tex]\( F \)[/tex], which represents degrees Fahrenheit.
- The function transforms [tex]\( F \)[/tex] using the formula [tex]\( \frac{5}{9}(F - 32) \)[/tex].

2. Function Purpose:
- The purpose of the formula is to convert the input temperature from Fahrenheit ([tex]\( F \)[/tex]) to Celsius ([tex]\( C \)[/tex]).
- The subtraction of 32 adjusts the Fahrenheit temperature to match the zero-point for Celsius, which is 0 degrees Celsius at 32 degrees Fahrenheit.

3. Calculate the Conversion:
- The expression inside the parenthesis, [tex]\( F - 32 \)[/tex], calculates how far the given Fahrenheit temperature is from freezing point in Celsius.
- Multiplying by [tex]\(\frac{5}{9}\)[/tex] converts the adjusted temperature to the Celsius scale.

4. Interpret the Output [tex]\( C(F) \)[/tex]:
- [tex]\( C(F) \)[/tex] gives the result in degrees Celsius. Therefore, the function's output is the equivalent temperature in Celsius after converting from the input Fahrenheit value.

5. Conclusion:
- Thus, [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.

Therefore, the statement that best describes [tex]\( C(F) \)[/tex] 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.