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------------------------------------------------ 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. The temperature of [tex]F[/tex] degrees Fahrenheit converted to degrees Celsius.
B. The temperature of [tex]F[/tex] degrees Celsius converted to degrees Fahrenheit.
C. The temperature of [tex]C[/tex] degrees Fahrenheit converted to degrees Celsius.
D. The temperature of [tex]C[/tex] degrees Celsius converted to degrees Fahrenheit.

Answer :

Sure! Let’s break down the problem step by step.

Siera wants to convert the average high temperature from degrees Fahrenheit to degrees Celsius using the function [tex]\(C(F) = \frac{5}{9}(F - 32)\)[/tex].

### Understanding the Function
- [tex]\(F\)[/tex] represents the temperature in degrees Fahrenheit.
- [tex]\(C(F)\)[/tex] is the result of the conversion, which represents the temperature in degrees Celsius.

To determine what [tex]\(C(F)\)[/tex] represents, let's interpret the function mathematically:
1. [tex]\(F\)[/tex] is the input to the function and it is the temperature in degrees Fahrenheit.
2. The function [tex]\(C(F)\)[/tex] converts this temperature from degrees Fahrenheit to degrees Celsius.

### Options Given
Let's look at the options and see which one correctly describes what [tex]\(C(F)\)[/tex] represents:
1. The temperature of [tex]\(F\)[/tex] degrees Fahrenheit converted to degrees Celsius.
2. The temperature of [tex]\(F\)[/tex] degrees Celsius converted to degrees Fahrenheit.
3. The temperature of [tex]\(C\)[/tex] degrees Fahrenheit converted to degrees Celsius.
4. The temperature of [tex]\(C\)[/tex] degrees Celsius converted to degrees Fahrenheit.

### Analysis of Each Option
- Option 1: This option correctly states that [tex]\(C(F)\)[/tex] is the conversion of the temperature [tex]\(F\)[/tex] (in degrees Fahrenheit) to degrees Celsius.
- Option 2: This option incorrectly states that [tex]\(F\)[/tex] is in degrees Celsius and being converted to Fahrenheit, which is not accurate as per the function.
- Option 3: This option suggests that [tex]\(C\)[/tex] is a temperature value in degrees Fahrenheit being converted, which does not match our function.
- Option 4: This option implies [tex]\(C\)[/tex] is a value in degrees Celsius being converted, which again does not match our function.

### Conclusion
The correct answer is:
The temperature of [tex]\(F\)[/tex] degrees Fahrenheit converted to degrees Celsius.

Thus, [tex]\(C(F)\)[/tex] represents the temperature of [tex]\(F\)[/tex] degrees Fahrenheit converted to degrees Celsius.