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 :

Certainly! To solve this problem, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] represents.

Let's break it down:

1. Understand the Formula:
- The function given, [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex], is a standard formula used for converting temperatures from degrees Fahrenheit to degrees Celsius.
- The formula works by first subtracting 32 from the Fahrenheit temperature. This adjustment accounts for the fact that 32 degrees Fahrenheit is the freezing point of water, which is 0 degrees Celsius.
- Then, multiplying the result by [tex]\(\frac{5}{9}\)[/tex] scales the adjusted temperature from the Fahrenheit scale to the Celsius scale.

2. Identify the Components:
- [tex]\( F \)[/tex] is the input to the function. It represents the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output of the function. It gives us the equivalent temperature in degrees Celsius.

3. Determine What [tex]\( C(F) \)[/tex] Represents:
- Since [tex]\( C(F) \)[/tex] provides the temperature in degrees Celsius when you input the temperature in degrees Fahrenheit, [tex]\( C(F) \)[/tex] represents the output in degrees Celsius for a given input [tex]\( F \)[/tex] in degrees Fahrenheit.

Therefore, the correct interpretation of [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.