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 understand what [tex]\( C(F) \)[/tex] represents, let's look at the function being used:

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

This function is a conversion formula used to change temperatures from degrees Fahrenheit to degrees Celsius. Here's how it works:

1. Input: The function takes an input [tex]\( F \)[/tex], which stands for the temperature in degrees Fahrenheit.

2. Conversion Process:
- First, it subtracts 32 from the Fahrenheit temperature.
- Then, it multiplies the result by [tex]\(\frac{5}{9}\)[/tex] to convert the temperature to degrees Celsius.

3. Output: The result of this calculation is [tex]\( C(F) \)[/tex], which represents the temperature in degrees Celsius.

Now, let's determine what [tex]\( C(F) \)[/tex] represents in terms of the options provided:

- Option 1: [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.

- Option 2: [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.

- Option 3: [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.

- Option 4: [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.

We can see that the first option correctly describes the process and result of this function: [tex]\(C(F)\)[/tex] is indeed the output in degrees Celsius when the input is [tex]\(F\)[/tex] in degrees Fahrenheit.

So, 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.