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Answer :
Sure! Let's go through the problem step by step:
Siera wants to convert her home town's average high temperature from degrees Fahrenheit (°F) to degrees Celsius (°C). To do this, she uses the function:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
Here, [tex]\( C(F) \)[/tex] is the expression used to find the temperature in degrees Celsius when the temperature in degrees Fahrenheit is [tex]\( F \)[/tex].
Let's break down the options given for what [tex]\( C(F) \)[/tex] represents:
1. Option 1: [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.
2. Option 2: [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.
3. Option 3: [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.
4. Option 4: [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.
Now, let's evaluate what each option means:
- Option 1: This correctly states that [tex]\( C(F) \)[/tex] gives us the temperature in degrees Celsius when we start with degrees Fahrenheit. This matches the formula provided.
- Option 2: This incorrectly reverses the roles of Celsius and Fahrenheit. [tex]\( C(F) \)[/tex] is not used to find Fahrenheit from Celsius; it’s the other way around.
- Option 3: This incorrectly states that [tex]\( C(F) \)[/tex] gives a temperature in degrees Fahrenheit when, in fact, it should be Celsius.
- Option 4: This incorrectly suggests using [tex]\( F \)[/tex] when that's part of the input, not the output.
Given our function and understanding, Option 1 is the correct representation of what [tex]\( C(F) \)[/tex] means—converting a temperature from degrees Fahrenheit to degrees Celsius.
Siera wants to convert her home town's average high temperature from degrees Fahrenheit (°F) to degrees Celsius (°C). To do this, she uses the function:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]
Here, [tex]\( C(F) \)[/tex] is the expression used to find the temperature in degrees Celsius when the temperature in degrees Fahrenheit is [tex]\( F \)[/tex].
Let's break down the options given for what [tex]\( C(F) \)[/tex] represents:
1. Option 1: [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.
2. Option 2: [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.
3. Option 3: [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.
4. Option 4: [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.
Now, let's evaluate what each option means:
- Option 1: This correctly states that [tex]\( C(F) \)[/tex] gives us the temperature in degrees Celsius when we start with degrees Fahrenheit. This matches the formula provided.
- Option 2: This incorrectly reverses the roles of Celsius and Fahrenheit. [tex]\( C(F) \)[/tex] is not used to find Fahrenheit from Celsius; it’s the other way around.
- Option 3: This incorrectly states that [tex]\( C(F) \)[/tex] gives a temperature in degrees Fahrenheit when, in fact, it should be Celsius.
- Option 4: This incorrectly suggests using [tex]\( F \)[/tex] when that's part of the input, not the output.
Given our function and understanding, Option 1 is the correct representation of what [tex]\( C(F) \)[/tex] means—converting a temperature from degrees Fahrenheit to degrees Celsius.
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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.
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