College

For one month, Siera calculated her hometown's average high temperature in degrees Fahrenheit. Convert that temperature 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 convert temperatures from degrees Fahrenheit to degrees Celsius, we use the function [tex]\( C(f) = \frac{5}{9}(f - 32) \)[/tex].

In this function:

- [tex]\( f \)[/tex] is the temperature in degrees Fahrenheit that you want to convert.
- [tex]\( C(f) \)[/tex] is the result of the conversion and it gives you the temperature in degrees Celsius.

Let's break down the function:

1. Subtract 32: The formula starts by taking the Fahrenheit temperature and subtracting 32 from it. This is because 32 degrees Fahrenheit corresponds to the freezing point of water, which is 0 degrees Celsius.

2. Multiply by [tex]\(\frac{5}{9}\)[/tex]: After subtracting 32, you multiply the result by [tex]\(\frac{5}{9}\)[/tex]. This fraction is the conversion factor that adjusts the scale from Fahrenheit to Celsius.

When we interpret what [tex]\( C(F) \)[/tex] represents:

- Input [tex]\( F \)[/tex]: This is the temperature value you plug into the function, given in degrees Fahrenheit.
- Output [tex]\( C(f) \)[/tex]: This is the result you get after performing the calculation, giving the temperature in degrees Celsius.

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. This means the correct interpretation of [tex]\( C(F) \)[/tex] is that it is the value of the temperature conversion from Fahrenheit to Celsius.

In summary, the correct answer 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.