Graph of a function

The set of ordered pairs \((x,f(x))\) formed by pairing each input in a function’s domain with its output. In the Cartesian plane, these pairs appear as points.

Function: A relation that assigns each input in its domain exactly one output. The graph records the input-output pairs that define a function.
Vertical line test: A test for whether a plane curve is the graph of a function of x. Every vertical line must meet the graph at most once.
Root of a function: An input at which a function's value is zero. Roots are precisely where the graph meets the horizontal axis.
Graph of a relation: The set of ordered pairs satisfying a relation between variables. A function graph is a relation's graph with at most one output per input.
Domain of a function: The set of inputs for which a function is defined. Each domain element contributes an input coordinate to the graph.
Implicit function: A function specified by a relation among variables rather than an explicit output formula. Its equation may define a curve that is not one function's graph.
Derivative: A quantity describing a function's instantaneous rate of change. The graph's tangent slope represents the derivative where it exists.
Table of values: A tabular listing of selected inputs and their corresponding outputs. It records sample pairs, while the graph includes every pair in the domain.
Cartesian coordinate system: A coordinate system that locates points using signed distances from perpendicular axes. It displays ordered input-output pairs as points in the plane.
Parametric equation: A representation of a curve using coordinates defined by one or more parameters. It can trace curves whose points do not form a single-valued graph of y in x.

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