Understanding Range in Mathematics: Exploring the Set of Possible Output Values of a Function

Range

In mathematics, the term “range” refers to the set of all possible output values of a function

In mathematics, the term “range” refers to the set of all possible output values of a function. It represents the variation or extent of the function’s values. Put simply, it is the collection of all values that the function can produce.

To determine the range of a function, you need to identify the set of output values that the function can generate for all possible input values. This can be done by analyzing the behavior of the function and considering its domain, which is the set of all possible input values.

Let’s consider an example to illustrate the concept of range. Suppose we have a function f(x) = x^2. In this case, the function takes an input value (x) and squares it to produce an output value.

To find the range of this function, we need to consider all possible input values and determine the corresponding output values. Since squaring a real number always results in a non-negative number, the output values of this function are always greater than or equal to zero.

Therefore, the range of the function f(x) = x^2 is the set of all non-negative real numbers, or [0, +∞). This means that the range includes zero and all positive real numbers, but does not include any negative numbers.

In general, determining the range of a function involves analyzing its properties and understanding the restrictions on its output values. It is also important to consider the domain of the function, as it can provide crucial information for identifying the range.

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