What is the difference between a domain and a range? Describe a real life situation thatcould be modeled by a function.
domain: the set of all possible input values of a relation
Range: the set of all possible output values.
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The domain and range are two important concepts in mathematics, specifically in the study of functions.
The domain of a function is the set of all possible input values or the values that can be plugged into a function to produce an output. It represents the independent variable(s) or the "x" values of a function.
The range, on the other hand, is the set of all possible output values or the values that are obtained by evaluating the function using the input values from the domain. It represents the dependent variable(s) or the "y" values of a function.
To better illustrate the difference between the domain and range, let's consider a real-life situation that can be modeled by a function. One example could be the relationship between the number of hours spent studying and the corresponding grade on a test.
In this case, the domain would consist of all possible values for the independent variable, which is the number of hours spent studying. It could be a range of values like 0, 1, 2, 3, and so on, up to a certain maximum number of hours one could study.
The range would then represent the possible grades that can be obtained based on the hours of studying. Let's say the grades could be percentages from 0 to 100, so the range would be all values between 0 and 100.
By analyzing this real-life situation, we can see that the domain and range help us understand the possible inputs (hours spent studying) and outputs (grades on the test) of the function that models this relationship.
So, to summarize, the domain refers to the set of all possible input values of a function, while the range refers to the set of all possible output values of the function.