Question

prompt
determine if the outside temperature is a function of the time of day or if the time of day is a function of temperature and explain why.

Explanation:

Step1: Define function concept

A function is a relation where for each input (independent - variable) there is exactly one output (dependent - variable).

Step2: Analyze temperature as function of time

For a given time of day (input), there is typically a single outside - temperature value (output). So, temperature \(T\) can be written as \(T(t)\) where \(t\) is time of day.

Step3: Analyze time as function of temperature

At different times of day, the same temperature can occur. For example, the temperature might be the same at 10 am and 4 pm on some days. So, for a single temperature value (input), there can be multiple time - of - day values (outputs), and time is not a function of temperature.

Answer:

The outside temperature is a function of the time of day. The time of day is not a function of the temperature.