What is the difference between domain and range? Describe a real life situation that could be modeled by a function.
The domain and range are terms used in mathematics to describe the inputs and outputs of a function.
The domain of a function refers to the set of all possible input values or independent variables. In simpler terms, it represents the values that you can plug into a function. For example, if we consider a function that represents the height of a person based on their age, the domain would consist of all possible ages a person can have, such as 0, 1, 2, 3, and so on.
The range of a function, on the other hand, refers to the set of all possible output values or dependent variables. It represents the values that the function can produce. In the same height example, the range would consist of all possible heights a person can have, such as 0 inches, 1 inch, 2 inches, and so on.
In summary, the domain represents the input values, while the range represents the output values of a function.
Now, let's consider a real-life situation that can be modeled by a function. One example could be a person's monthly income based on their years of experience. In this case, the years of experience would be the independent variable, or the domain, and the corresponding monthly income would be the dependent variable, or the range.
To model this situation as a function, you would gather data of different individuals with their corresponding years of experience and monthly income. By plotting these points on a graph and connecting them with a line or curve, you can visualize the relationship between years of experience and monthly income. This curve or line would represent the function that models this real-life situation.