What is Domain and Range?

Mathematical functions are analogous to vending (soda) machine operations. When you put in a certain amount of money, you can choose from a variety of sodas. Similarly, when we use functions, we enter different numbers and get new numbers as a result. The primary characteristics of functions are domain and range. A soda can be purchased with quarters or one-dollar bills.

If you put in pennies, the machine will not give you any soda flavor. As a result, the domain represents the inputs available here, which are quarters and one-dollar bills. A cheeseburger will not be served from a soda machine, no matter how much you pay.

Domain of a Function

A domain can be defined as “all the values” that make up a function. A function’s domain is the set of all possible inputs to the function. Consider this box to be a function with f(x) = 2x. When the values x = {1,2,3,4,…} are entered, the domain is simply the set of natural numbers, and the output values are referred to as the range.

How To Find The Domain of a Function?

• To determine the domain, we must examine the values of the independent variables that are permitted to be used, as explained above, namely no zero at the bottom of the fraction and no negative sign inside the square root.
• Subject to some constraints, the domain of a function is generally considered to be the set of all real numbers (R). They are as follows:
• The domain is “the set of all real numbers” when the given function is of the form f(x) = 2x + 5 or f(x) = – 2.
  The domain is the set of all real numbers except one when the given function is of the form f(x) = 1/(x – 1).
• In some cases, the interval is specified alongside the function, for example, f(x) = 3x + 4, 2 x 12. In this case, x can accept values ranging from 2 to 12. (i.e. domain).
• Domain constraints are the values for which the given function cannot be defined.

Range of a Function

A function’s range is the set of all its outputs. Example: Consider the function f: A→ B, where f(x) = 2x and A and B are natural number sets. In this case, A is said to be the domain, and B is said to be the co-domain. The range is then obtained as the function’s output.

The range is defined as a set of even natural numbers. The domain elements are referred to as pre-images, and the co-domain elements that are mapped are referred to as images. In this case, the range of the function f is the set of all images of domain elements (or) the set of all function outputs.

Range And Domain in Real Life

When you have a distribution with no extreme values, the range is a good indicator of variability. When combined with measures of central tendency, the range can provide information about the distribution’s span. However, when you have outliers in your data set, the range can be misleading.

The range tells us how many bags of chips we can get based on the amount of money we have and how much we spend. Once again, the domain and range provide extremely important information about the real-world situation of purchasing a product with a limited budget.

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