Difference Between Domain and Range
To understand the two concepts of domain and range, one needs to understand what is meant by a mathematical function. A function is a unique relation between two sets of variables, wherein one set completely determines what the other set will be and every element in the first set has an associated unique element in the other set. I assume that you know what are dependent and independent variables. The variables of the first set are known as independent variables while second set variables are dependent ones. For example, consider the function ‘y = x + 5′. Here ‘x’ is the independent variable while y is dependent. For every integral value of x, y has a unique fixed value. In defining function, I have already defined what a domain and range of function is. Let us see what exactly they are.
Domain is the set of all values that an independent variable of a function can take. The range is the corresponding set of values determined by entering domain values in the function. In the above function, (y = f (x) = x + 5), the independent variable x can take all the real number values and hence its domain is the set of all real numbers. For each value of x, corresponding dependent variable values are also real numbers, which means that range of this function is the set of all real numbers.
Consider one more example. Let the function be ‘y = 1 / (1 – x)’ and you need to find the domain for this function. As you can see, for x = 1, the function is undefined. However, for all other values it is defined and can be calculated. Hence, the domain of this function is the set of all real numbers except the value of x which is 1. Also the set of values of ‘y’, for every x are again real numbers. Therefore range of this function will also be a set of real numbers. To accurately know the range of a function, you need to draw a graph. You could also use mathematical software programs that can plot functions for you. You also might want to know what is the difference between an equation and an expression.
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