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 tackle this question, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is doing. Let's break it down step by step:

1. Identify the function: The function provided is [tex]\( C(F) \)[/tex]. Here, [tex]\( C \)[/tex] represents Celsius, and [tex]\( F \)[/tex] represents Fahrenheit. This means that this function is used to convert a temperature from degrees Fahrenheit to degrees Celsius.

2. Understand the components:
- The formula starts by taking the input [tex]\( F \)[/tex], which is the temperature in degrees Fahrenheit, and subtracting 32 from it. This is because the Fahrenheit scale's zero point is 32 degrees above the Celsius zero point.
- The result is then multiplied by [tex]\( \frac{5}{9} \)[/tex]. This fraction is the conversion factor between the Fahrenheit and Celsius scales, relating how the increments differ between the two scales.

3. Determine the output: The output of the function, [tex]\( C(F) \)[/tex], is the result of this calculation, which is the temperature value converted into degrees Celsius.

4. Translate the function's purpose:
- [tex]\( C(F) \)[/tex] stands for the temperature in degrees Celsius, which is computed by applying the conversion formula to a temperature originally measured in degrees Fahrenheit.

So, the correct interpretation of what [tex]\( C(F) \)[/tex] represents 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.

This matches with the concept that we're converting Fahrenheit temperatures to Celsius using this specific formula.