Question

Explain why \(F=\frac{9}{5} C+32\) represents a function.

Short answer

The formula \(F=\frac{9}{5} C+32\) is a function because for each input (Celsius temperature), it produces exactly one output (Fahrenheit temperature).

Step-by-step solution

Define the Function

The formula given is \(F=\frac{9}{5} C+32\), which is a function that maps the temperature in degree Celsius (C) to degree Fahrenheit (F).

Verify Each Input Has Exactly One Output

We can verify that this formula is indeed a function by checking that for each given value of C, there is exactly one value of F. This is true because for any specific value of C that you input into the formula, you'll always get one and only one output value of F. This formula doesn't have any variables other than C in it, meaning for each C, there can only be one F.

Conclusion

Therefore, \(F=\frac{9}{5} C+32\) is a function since each input has exactly one output. It fulfills the definition of a function.