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 :

Certainly! Let's explore what [tex]\( C(F) \)[/tex] represents step-by-step.

The function given is:

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

1. Understanding the Function:
This function is used to convert temperatures from degrees Fahrenheit to degrees Celsius.

2. Understanding the Inputs and Outputs:
- The input to this function is [tex]\( F \)[/tex], which represents the temperature in degrees Fahrenheit.
- The output of this function is [tex]\( C(F) \)[/tex], which represents the temperature in degrees Celsius.

3. Conversion Explanation:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a standard formula for converting Fahrenheit to Celsius.
- The term [tex]\( F - 32 \)[/tex] adjusts for the difference in the zero points of the two scales.
- Multiplying by [tex]\( \frac{5}{9} \)[/tex] converts the temperature difference from the Fahrenheit scale to the Celsius scale.

4. Conclusion:
Therefore, [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex], which gives the temperature in degrees Celsius when the input [tex]\( F \)[/tex] is the temperature in degrees Fahrenheit.

Thus, the correct interpretation of [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."