To determine if the relationship between Celsius ([tex]\( C \)[/tex]) and Fahrenheit ([tex]\( F \)[/tex]) temperatures described by the equation [tex]\( F = \frac{9}{5}C + 32 \)[/tex] is a function, let's delve into the definition of a mathematical function.
### Step-by-Step Solution
1. Understanding the Equation:
- The given equation is [tex]\( F = \frac{9}{5}C + 32 \)[/tex]. This converts a temperature from Celsius to Fahrenheit.
2. Definition of a Function:
- A relationship is considered a function if each input has exactly one unique output.
- In other words, for every value of [tex]\( C \)[/tex], there should be exactly one corresponding value of [tex]\( F \)[/tex].
3. Analyzing the Equation:
- With the equation [tex]\( F = \frac{9}{5}C + 32 \)[/tex], let's consider any particular value for [tex]\( C \)[/tex].
- The equation provides a unique value for [tex]\( F \)[/tex] for each [tex]\( C \)[/tex]. For example:
- If [tex]\( C = 0 \)[/tex], then [tex]\( F = \frac{9}{5}(0) + 32 = 32 \)[/tex].
- If [tex]\( C = 100 \)[/tex], then [tex]\( F = \frac{9}{5}(100) + 32 = 180 + 32 = 212 \)[/tex].
Thus, since for every value of [tex]\( C \)[/tex] (Celsius temperature), there is exactly one corresponding [tex]\( F \)[/tex] (Fahrenheit temperature), this relationship meets the criteria of a function.
### Conclusion
It is a function because every Celsius temperature is associated with only one Fahrenheit temperature.
