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 :

Sure! Let's go through the question step-by-step to understand what [tex]$C(F)$[/tex] represents.

We are given a function to convert temperature from degrees Fahrenheit (F) to degrees Celsius (C), which is defined as:

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

Here, [tex]\( C(F) \)[/tex] is the function used to make the conversion. Let's break down what each part means:

1. Function Name and Input: The function is named [tex]\( C \)[/tex], and it takes [tex]\( F \)[/tex] as the input variable. In this context, [tex]\( F \)[/tex] represents a temperature value in degrees Fahrenheit.

2. Inside the Function: The expression [tex]\( F - 32 \)[/tex] is used to account for the offset between the Fahrenheit and Celsius scales. Multiplying by [tex]\(\frac{5}{9}\)[/tex] adjusts the difference to translate it into the Celsius scale.

3. Output of the Function: The entire expression [tex]\(\frac{5}{9}(F - 32)\)[/tex] gives us the equivalent temperature in degrees Celsius when we input a temperature in degrees Fahrenheit.

Now, looking at our options:
- We need to determine what [tex]\( C(F) \)[/tex] represents.

Let's evaluate the first option:
- "C(F) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit."

This option accurately describes what's happening. The function [tex]\( C(F) \)[/tex] takes Fahrenheit temperature as input and converts it to Celsius, providing us with the temperature in degrees Celsius as its output.

Therefore, the correct description 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.

This matches the setting of a temperature conversion function from Fahrenheit to Celsius.