Understanding the Range in Mathematics | Exploring the Set of Possible Output Values of Functions and Relations

Range

In mathematics, the range refers to the set of all possible output values of a function or relation

In mathematics, the range refers to the set of all possible output values of a function or relation. Simply put, it represents the collection of all values that the dependent variable can take on.

To determine the range of a function or relation, you need to examine the outputs or the y-values. You look at all the possible values that the dependent variable can be when the independent variable varies across its domain. It is important to note that the range consists of distinct values, meaning each value can only occur once in the set.

To illustrate this concept, let’s consider a simple example. Suppose we have a function f(x) = x^2, where x represents the input values and f(x) represents the output values. When we square different numbers as input, such as -2, 0, and 2, the output values would be 4, 0, and 4, respectively. In this case, the range of the function f(x) = x^2 would be {0, 4}, as these are the only possible output values.

However, it’s important to note that not all functions have well-defined ranges. Some functions may have infinite ranges, where the output values can extend infinitely in a particular direction. For example, in the function f(x) = 2x, as x gets larger or smaller, the y-values also grow or decrease without bound. In such cases, we denote the range as (-∞, ∞) or sometimes use an extended notation to indicate the type of infinity, like (-∞, +∞) or [0, ∞).

In summary, the range is a fundamental concept in mathematics that describes the set of all possible output values of a function or relation. It allows us to understand the scope and behavior of functions by analyzing the possible values that the dependent variable can assume.

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