College

For one month, Siera calculated her hometown's average high temperature in degrees Fahrenheit. She converted 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.

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 :

Let's break down the question and the problem step-by-step:

The function provided is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This equation is used to convert temperature from degrees Fahrenheit to degrees Celsius. Here's what each part represents:

1. [tex]\( F \)[/tex]: The input to the function, which is the temperature in degrees Fahrenheit.
2. [tex]\( C(F) \)[/tex]: The output of the function, which gives the temperature in degrees Celsius.

The question asks what [tex]\( C(F) \)[/tex] represents. To determine this, let's analyze the function and consider what is happening:

- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] specifically computes the temperature in Celsius from a given Fahrenheit measurement.
- Therefore, when you input a temperature [tex]\( F \)[/tex] (in degrees Fahrenheit), the function converts it and gives you the output temperature [tex]\( C(F) \)[/tex] (in degrees Celsius).

To better understand, let's look at an example. Suppose the temperature is 86 degrees Fahrenheit. Calculate the Celsius temperature using the given formula:

[tex]\[ F = 86 \][/tex]

Using the conversion formula:

[tex]\[ C = \frac{5}{9}(86 - 32) \][/tex]

Simplifying inside the parentheses first:

[tex]\[ 86 - 32 = 54 \][/tex]

Now multiply by [tex]\(\frac{5}{9}\)[/tex]:

[tex]\[ C = \frac{5}{9} \times 54 = 30 \][/tex]

So, 86 degrees Fahrenheit is equal to 30 degrees Celsius.

This means that [tex]\( C(F) \)[/tex] gives us 30 degrees Celsius when the input [tex]\( F \)[/tex] is 86 degrees Fahrenheit.

With this understanding, the correct choice 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.