What is the difference between domain and range? Describe a real-life situation that could be modeled by a function
An example of a domain is how many gallons of gas are in a car's gas tank (say, 0 to 15 gallons) and the range would be how far that can drive with what is initially in the tank.
"Domain" describes the values that an independent variable can have, and "range" is the resulting set of dependent variable values that correspond to the domain.
The domain and range are both concepts used in mathematics, specifically in relation to functions.
The domain of a function is the set of all possible input values, or the set of independent variables. In simpler terms, it is the set of values for which the function is defined. It represents the values that can be plugged into the function to produce a valid output.
The range of a function is the set of all possible output values, or the set of dependent variables. It is the set of values that can be obtained by evaluating the function with different input values from its domain.
To illustrate this concept with a real-life situation, let's consider a function that represents the relationship between time spent studying and test scores. In this scenario, the domain could represent the time spent studying, while the range represents the corresponding test scores.
For example, let's say you are studying for a test and you want to know how your test score will be affected by the time you spend studying. The time you spend studying will be the input values, or the domain. The test scores you achieve based on the different amounts of study time will be the output values, or the range.
For instance, if you spend 2 hours studying, your score might be 70. If you study for 5 hours, your score might increase to 85. In this case, the domain would be the set of possible study times (e.g., 2 hours, 5 hours), and the range would be the set of corresponding test scores (e.g., 70, 85).
By studying this relationship over a range of input values, you can create a function that models the real-life situation and predicts test scores based on the time spent studying.
The domain and range are fundamental concepts in mathematics, particularly in relation to functions.
The domain is the set of all possible input values or independent variables of a function. It represents the values for which the function is defined or valid. It determines the base on which the function operates. In simpler terms, the domain specifies the acceptable inputs for a function.
On the other hand, the range is the set of all possible output values or dependent variables that a function can produce. It represents the values that the function can generate based on its input values. In essence, the range showcases the possible outputs or results of a function.
To describe a real-life situation that can be modeled by a function, let's consider the example of a car rental company. Suppose the company charges customers based on the number of days they keep the rented car.
Let's define a function (let's call it "Cost") that relates the number of days (d) to the total cost (c) of renting a car. The function would have a specific formula or rule that connects the two variables.
For instance, this function could be modeled as follows:
Cost(d) = 40 + 30d
In this scenario, the domain of the function would represent the possible values for the number of days (d) a customer can keep the car, considering restrictions such as minimum or maximum rental periods. The range, in turn, would represent the possible cost (c) values that the function can generate, covering the total cost of renting the car for different durations.
By understanding the domain and range of this function, the car rental company can accurately calculate the cost for any given number of days a customer chooses to rent a car.