Codomain

The codomain of a function is the specified set in which its outputs are required to lie. It may include elements the function never outputs.

Function: A relation that assigns each element of a domain exactly one element of a codomain. A codomain is specified as part of a function’s domain-to-target description.
Surjective function: A function whose image equals its codomain. Surjectivity tests whether every element of the specified target is reached.
Range of a function: A term often used for the set of values a function takes, though conventions vary. Unlike the codomain, the range is often used to mean the image.
Exponential function: A function of the form f(x)=aˣ, where a is a positive constant other than one. Over the real numbers, its positive outputs make the choice of codomain consequential.
Domain of a function: The set of inputs for which a function is defined. The domain and codomain together specify the sets a function maps between.
Injective function: A function that maps distinct inputs to distinct outputs. Injectivity concerns collisions among outputs, independently of unused codomain elements.
Partial function: A function that is defined only on a subset of a proposed domain. Its possible outputs remain distinct from the inputs where it is defined.
Logarithm: The inverse operation to exponentiation, defined for positive real inputs. Its real-valued domain corresponds to the positive range of the real exponential function.
Image of a function: The set of values a function actually takes on its domain. The image is contained in the codomain and can be smaller than it.
Bijective function: A function that is both injective and surjective. Bijectivity requires the codomain to match the image and each output to have one input.

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