Image (mathematics)

The image of a function on a specified domain subset is the set of all outputs the function produces from inputs in that subset.

Function: A relation that assigns each input in a domain exactly one output. An image collects the outputs assigned by a function.
Set-builder notation: A notation that defines a set by stating the properties its elements satisfy. It expresses an image by collecting function values over chosen inputs.
Surjective function: A function whose image equals its codomain. Surjectivity is precisely the condition that every declared output is attained.
Inverse function: A function that reverses the input-output assignments of another function. An inverse function can exist on the image when the original function is injective.
Domain (mathematics): The set of inputs for which a function is defined. Changing the selected inputs can change the image.
Image of a set: The set of values a function takes on elements of a specified set. This is the image construction applied to a particular subset of the domain.
Injective function: A function that maps distinct inputs to distinct outputs. Its image retains enough information to identify each input uniquely.
Graph of a function: The set of ordered input-output pairs that defines a function's assignments. The graph records inputs alongside outputs; the image retains outputs alone.
Codomain: A specified set in which a function's outputs are declared to lie. The image is contained in the codomain but need not equal it.
Preimage: The set of inputs that a function maps into a specified set of outputs. Preimages reverse the direction of the set-mapping operation.

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