What is the difference between domain and range?
A domain is the set of numbers which are valid values for the independent variable. The range is the set of valid numbers for the dependent variable.
The angle of the sun over the horizon over the course of the day would be fairly easy to model. The domain would be the hours between sunrise and sunset and the range would be 0 to whatever is the maximum elevation of the sun is on a given day on any particular latitude. For instance, during the equinox, at a latitude of 50 degrees North, the maximum angle of the sun above the horizon is 40 degrees and therefore the range would be 0 to 40 degrees. Notice that the range will increase during the summer and decrease during the winter.
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The difference between domain and range lies in their definitions and how they are used in mathematics.
The domain of a function refers to the set of all possible input values (or independent variables) for the function. In simple terms, it represents all the values that you can plug into a function. For example, if we have a function f(x) = 2x + 3, the domain would be all real numbers because you can substitute any value for x and get a valid output.
On the other hand, the range of a function represents the set of all possible output values (or dependent variables) that the function can produce. It defines the entire set of values that the function can output based on its defined domain. Continuing with our previous example, the range would also be all real numbers because, for any value of x that you choose, the function f(x) will produce a corresponding y value.
To determine the domain and range of a function, here are some steps to follow:
1. Identify the function and its variables: Start by understanding the given function and its variables. For example, if you have a function y = f(x), the variable "x" is typically the independent variable, and "y" is the dependent variable.
2. Determine the domain: Consider any possible restrictions on the independent variable. Look for values that may cause problems, such as division by zero or taking the square root of a negative number. Exclude these values from the domain. Otherwise, if there are no restrictions, the domain will usually be all real numbers.
3. Find the range: Analyze the values that the function outputs as the independent variable varies. Identify the highest and lowest possible values that the dependent variable can take. The range will include all these possible outputs.
4. Write the domain and range: Once you have determined the possible values for the independent variable (domain) and the dependent variable (range), express them in the appropriate notation. The domain is typically written as a set of numbers or an interval, while the range is also presented as a set or interval.
In summary, the domain refers to the set of all possible inputs of a function, while the range defines the set of all possible outputs. Determining the domain and range involves analyzing the restrictions and output values of the function.