What is the difference between a domain and a range? Describe a real life situation that could be modeled by a function.
The domain and range are key concepts in mathematics, specifically in relation to functions. Let's start by understanding each term individually.
The domain of a function is the set of all possible input or independent values for the function. In simpler terms, it represents all the values that can be plugged into a function to get an output.
The range of a function is the set of all possible output or dependent values for the function. In more straightforward words, it represents all the values that the function can produce as a result.
To illustrate this concept, let's consider a real-life situation that can be modeled by a function:
Imagine you work for a food delivery service and you are responsible for calculating the delivery time based on the distance between the restaurant and the customer's location. Let's say the function f represents this scenario, where f(x) represents the delivery time in minutes and x represents the distance in kilometers.
In this case:
- The domain would be the set of all possible distances between the restaurant and customer's location, such as {0 km, 1 km, 2 km, 3 km, ...}.
- The range would be the set of all possible delivery times, like {0 minutes, 5 minutes, 10 minutes, 15 minutes, ...}.
With this function, you can plug in different distances (domain) to calculate the corresponding delivery times (range). For example, if the restaurant is 2 km away from the customer, the function may output a delivery time of 10 minutes.
To summarize, the domain refers to the set of input values, while the range represents the set of output values that a function can produce. Real-life situations, like the food delivery example, can be represented and analyzed using functions to understand the relationship between variables and their possible outcomes.