Home > Graph of a function
In mathematics, the graph of a function is the collection of all pairs (x, f(x)) of the function. In particular graph means the graphical representation of this collection, in the form of a curve, together with axes, etc. Graphing is sometimes referred to as curve sketching. The graph of the function
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is {(1,a), (2,d), (3,c)}.
The graph of the cubic polynomial on the real line
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is {(x,x3-9x) : x is a real number}. If the set is plotted on a Cartesian plane, the result is
Therefore the graph of a function on real numbers is identical to the graphic representation of the function. For general functions, the graphic representation cannot be applied and the formal definition of the graph of a function suits the need of mathematical statements, e.g., the closed graph theorem in functional analysis.
The concept of the graph of a function is generalised to the graph of a relation. Note that although a function is always identified with its graph, they are not the same because it will happen two functions with different codomain could have the same graph. For example, the cubic polynomial mentioned above is a surjection if its codomain is the real numbers but it is not if its codomain is the complex field.
See also
- concavity
- critical point
- derivative
- graphing calculator
- stationary point
- slope
- solution pointIn mathematics, the solution point is a point that satisfies an equation. For example, the point (2,1) is a solution point of the equation 4''x + y 9 because if x 2 and y 1 then 4''x + y 4· 2 + 1 8 + 1 9. Some equations have no solution points — for examp
- vertical translationIn function graphing, a vertical translation is a related graph which, for every point x y ; has a y value which differs from another graph, by exactly some constant c''. For example, the antiderivatives of a family are vertical translations of each other
- y-interceptThe y-intercept in 2-D space is the point where graph of a function or relationship intercepts the y-axis of the coordinate system. If the function is specified in form y f(x), the y-intercept is easy to find by calculating f(0). For example, in linear eq
