What is range in math?

In mathematics, the range refers to the set of all possible output values (y-values) that a function or relation can produce. It's also often referred to as the image of the function.

• Understanding the Concept: The range is closely related to the <a href="https://www.wikiwhat.page/kavramlar/domain%20of%20a%20function">domain of a function</a>, which represents the set of all possible input values (x-values). While the domain dictates what values can be plugged into a function, the range describes what values come out of the function.

• Determining the Range: Finding the range can involve different techniques depending on the type of function. For simple functions, it might be possible to determine the range by inspection. For more complex functions, techniques like graphing, using algebraic manipulations, or analyzing the function's behavior as x approaches positive or negative infinity may be required.

• Range in different functions: The <a href="https://www.wikiwhat.page/kavramlar/range%20of%20quadratic%20functions">range of quadratic functions</a> is determined by its vertex.

• Notation: The range is typically expressed as a set of values, an interval, or a union of intervals. For example, the range of the function f(x) = x² is [0, ∞), because the output values are always greater than or equal to zero.

• Relationship to Codomain: The range is a subset of the <a href="https://www.wikiwhat.page/kavramlar/codomain">codomain</a>. The codomain specifies the set of all possible potential output values, while the range specifies the set of values that are actually produced.