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 :

Sure! Let's explore what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used for and what it represents.

1. Understanding the Function:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a mathematical expression used to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C).
- Here, [tex]\( F \)[/tex] is the temperature in Fahrenheit, which we input into the function.
- [tex]\( C(F) \)[/tex] calculates the corresponding temperature in Celsius.

2. Breaking Down the Formula:
- The formula subtracts 32 from the Fahrenheit temperature. This is because 32°F corresponds to 0°C, which is the freezing point of water.
- The result is then multiplied by [tex]\( \frac{5}{9} \)[/tex], which is the ratio used to convert the scale from Fahrenheit to Celsius.

3. What Does [tex]\( C(F) \)[/tex] Represent?
- Since [tex]\( C(F) \)[/tex] is giving us a value in Celsius when we start with a value in Fahrenheit, it represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.

Given these steps, 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. This explanation should help clarify how Fahrenheit is converted to Celsius using this formula.