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 break down the function [tex]$C(F) = \frac{5}{9}(F - 32)$[/tex]. This is a formula used to convert temperatures from Fahrenheit (F) to Celsius (C). In this function:

1. Input (F): The variable [tex]$F$[/tex] represents the temperature in degrees Fahrenheit. This is the starting point or input for the function, which you want to convert.

2. Function (C(F)): The function itself, [tex]$C(F)$[/tex], takes this Fahrenheit input, applies the conversion formula, and outputs a result.

3. Output (C(F)): The result of the function, [tex]$C(F)$[/tex], is the temperature in degrees Celsius. This is what the function calculates after performing the conversion using the formula.

Now, let's match this understanding with the given answer choices:

- 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."
This statement is correct: it accurately describes that [tex]$C(F)$[/tex] is the Celsius temperature output when [tex]$F$[/tex] is the Fahrenheit temperature input.

- Option 2, 3, and 4: These statements are incorrect because they either mix up the roles of Celsius and Fahrenheit or confuse the function's input and output.

Therefore, the correct interpretation of [tex]$C(F)$[/tex] from the given options is:

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."