Exploring the Mathematical Concept of Range | Understanding the Set of Possible Outputs of a Function

range

In mathematics, the term “range” refers to the set of all possible outputs or values that a function can produce

In mathematics, the term “range” refers to the set of all possible outputs or values that a function can produce. It represents the entire interval or set of values that the dependent variable can take on in relation to the independent variable.

More formally, the range of a function can be defined as the set of all possible values of the dependent variable (output) when the independent variable (input) is allowed to vary over its entire domain. It is the collection of all values that the function can reach or “map” to.

To find the range of a function, you typically start by determining the domain (all possible inputs) and then evaluating the function for different input values. The resulting set of output values forms the range.

For example, let’s consider the function f(x) = x^2. The domain of this function can be any real number, as there are no restrictions on the input. By evaluating the function for different values of x, we obtain a set of output values. In this case, as x varies, f(x) will always be greater than or equal to zero since squaring a number always results in a non-negative value. Therefore, the range of this function is the set of all non-negative real numbers, or [0, ∞).

It’s important to note that the range of a function can also be bounded or unbounded. A bounded range means that the function outputs values that are limited to a certain interval or set of values. An unbounded range, on the other hand, means that the function can produce values that extend indefinitely in one or both directions.

Understanding the range of a function is crucial in many mathematical applications, such as determining the maximum or minimum values of a function, analyzing the behavior of functions, and solving various types of equations and inequalities.

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