Question

the temperature in degrees celsius, \\(c\\), can be converted to degrees fahrenheit, \\(f\\), using the equation \\(f = \frac{9}{5}c + 32\\). which statement best describes if the relation \\((c, f)\\) is a function?

• it is a function because \\(-40^\circ\text{c}\\) is paired with \\(-40^\circ\text{f}\\).
• it is a function because every celsius temperature is associated with only one fahrenheit temperature.
• it is not a function because \\(0^\circ\text{c}\\) is not paired with \\(0^\circ\text{f}\\).
• it is not a function because some celsius temperatures cannot be associated with a fahrenheit temperature.

Explanation:

Analyze the definition of a function

$$ \text{A relation } (c, f) \text{ is a function if each input } c \text{ maps to exactly one output } f. $$

Evaluate the given equation

$$ f = \frac{9}{5}c + 32 $$

$$ \forall c \in \mathbb{R}, \quad \exists! f \in \mathbb{R} \text{ such that } f = \frac{9}{5}c + 32 $$

Match with the correct statement

$$ \text{Option 2: It is a function because every Celsius temperature is associated with only one Fahrenheit temperature.} $$

Answer:

• It is a function because \(-40^\circ\text{C}\) is paired with \(-40^\circ\text{F}\).
• It is a function because every Celsius temperature is associated with only one Fahrenheit temperature. (Correct answer)
• It is not a function because \(0^\circ\text{C}\) is not paired with \(0^\circ\text{F}\).
• It is not a function because some Celsius temperatures cannot be associated with a Fahrenheit temperature.