High School

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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 :

To understand what [tex]\( C(F) \)[/tex] represents in the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex], let’s go through the steps to convert a temperature from Fahrenheit to Celsius.

### Step-by-Step Explanation:

1. Formula Understanding:
- The given function is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
- This function is used for converting temperatures from Fahrenheit to Celsius.

2. Breaking Down the Formula:
- In the formula, [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- The expression [tex]\( (F - 32) \)[/tex] adjusts the Fahrenheit temperature by subtracting 32 because the freezing point of water is 32°F.
- The factor [tex]\( \frac{5}{9} \)[/tex] is used to convert the adjusted temperature difference from the Fahrenheit scale to the Celsius scale.

3. Conversion Process:
- When you input a temperature in Fahrenheit (denoted as [tex]\( F \)[/tex]) into the function [tex]\( C(F) \)[/tex], the function first subtracts 32 from [tex]\( F \)[/tex].
- Then, it multiplies the result by [tex]\( \frac{5}{9} \)[/tex], converting the temperature from Fahrenheit units to Celsius units.

4. Meaning of [tex]\( C(F) \)[/tex]:
- [tex]\( C(F) \)[/tex] provides the corresponding temperature in degrees Celsius after converting from the given temperature in degrees Fahrenheit.

### Conclusion:
Given this understanding, the correct interpretation of [tex]\( C(F) \)[/tex] is:

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

This tells us that when we input a temperature in degrees Fahrenheit into the function, the output is the equivalent temperature in degrees Celsius.