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 :

Certainly! Let's look at the function and what it represents.

Siera wants to convert a temperature from degrees Fahrenheit to degrees Celsius using the function:

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

Let's break down what each part means:

1. Function Definition: The function is written as [tex]\( C(F) \)[/tex], which typically means that [tex]\( C \)[/tex] is a function of [tex]\( F \)[/tex]. Here, [tex]\( F \)[/tex] is the input or the variable representing the temperature in degrees Fahrenheit.

2. Expression inside the Function: The expression [tex]\(\frac{5}{9}(F - 32)\)[/tex] is the formula used to convert Fahrenheit to Celsius.

3. Variables and Outputs:
- [tex]\( F \)[/tex] is the value in degrees Fahrenheit that you start with.
- [tex]\( (F - 32) \)[/tex] accounts for the difference between the two temperature scales’ starting points.
- [tex]\(\frac{5}{9}\)[/tex] is the conversion factor from Fahrenheit to Celsius.

4. Result of the Function [tex]\( C(F) \)[/tex]: The result, [tex]\( C(F) \)[/tex], represents the temperature in degrees Celsius after applying the conversion formula.

Given all this, we can determine which statement correctly defines what [tex]\( C(F) \)[/tex] represents:

- [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.

So, the correct interpretation is that:

[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.