give an example of a function that you might encounter in everyday life and describe its domain and range.
One example of a function that you might encounter in everyday life is the distance-time function when traveling by car. In this function, the input (or domain) represents the time it takes to travel, and the output (or range) represents the distance traveled.
Let's say you are taking a road trip and you want to know how far you will travel based on the time spent driving. For simplicity, let's assume a constant speed. In this case, the distance-time function could be represented as:
Distance = Speed × Time
The domain of this function would be the possible values for time, which generally starts from zero and can extend to the total time you plan to drive. For example, if you plan to drive for 5 hours, the domain would be [0, 5].
The range of the function would be the distances you can possibly travel within that time. It depends on your driving speed, but theoretically, the range can extend from zero (when you haven't started driving yet) to any distance you can cover within the given time.
It's important to note that this is a simplified example, and in reality, factors such as traffic, stops, or speed variations may affect the actual distance covered. However, the distance-time function can still provide a general approximation that helps plan trips or estimate travel times.