Understanding Range in Mathematics | Explained with Examples and Notations

Range

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

In mathematics, the term “range” refers to the set of all possible output values produced by a function. More specifically, it is the collection of all values that the dependent variable (output) can take on when given different inputs from the domain.

To understand range, let’s consider a simple example. Suppose we have a function that takes a number as an input and squares it. The domain of this function could be all real numbers because we can square any real number. However, the range would be only the set of non-negative real numbers since squaring a number always results in a positive value or zero.

The range is often expressed using set notation or interval notation. For instance, if we are given a function f(x) = x^2, we can write the range as:
Range = {y ∈ ℝ | y ≥ 0}

Here, this notation implies that the range consists of all real numbers (y) such that y is greater than or equal to zero.

It is important to note that not all functions have a range that includes all real numbers. Some functions may have restrictions on their domain or limitations on their output values. For example, the range of a function that calculates students’ test scores cannot exceed 100 since scores are typically measured on a scale of 0 to 100.

To find the range of a function, you can analyze its graph or use algebraic techniques depending on the type of function and the information provided.

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