# Graph of a function

**graphgraphsgraphingthree-dimensional graphplottinggraph of the functioncurveEquation Graphingfunction graphinggraphical**

In mathematics, the graph of a functionwikipedia

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### Function (mathematics)

**functionfunctionsmathematical function**

In mathematics, the graph of a function

, called the graph of the function.

### Continuous function

**continuouscontinuitycontinuous map**

are real numbers, these pairs are Cartesian coordinates of points in the Euclidean plane and thus form a subset of this plane, which is a curve in the case of a continuous function.

A real function, that is a function from real numbers to real numbers can be represented by a graph in the Cartesian plane; such a function is continuous if, roughly speaking, the graph is a single unbroken curve whose domain is the entire real line.

### Surface (mathematics)

**surfacesurfaces2-dimensional shape**

. For a continuous real-valued function of two real variables, the graph is a surface.

This is the case of the graph of a continuous function of two variables.

### Plot (graphics)

**plotdata plotplots**

In the simplest case one variable is plotted as a function of another, typically using rectangular axes; see Plot (graphics) for details.

A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables.

### Vertical line test

**a vertical line in general**

To test whether a graph of a relation represents a function of the first variable x, one uses the vertical line test.

In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not.

### Horizontal line test

To test whether a graph represents a function of the second variable y, one uses the horizontal line test.

Given a function (i.e. from the real numbers to the real numbers), we can decide if it is injective by looking at horizontal lines that intersect the function's graph.

### Curve

**closed curvespace curvesmooth curve**

are real numbers, these pairs are Cartesian coordinates of points in the Euclidean plane and thus form a subset of this plane, which is a curve in the case of a continuous function.

In particular, the length s of the graph of a continuously differentiable function y = f(x) defined on a closed interval [a,b] is

### Graphing calculator

**graphing calculatorsGraphinggraphical calculator**

A graphing calculator (also graphics calculator or graphic display calculator) is a handheld computer that is capable of plotting graphs, solving simultaneous equations, and performing other tasks with variables.

### Cartesian coordinate system

**Cartesian coordinatesCartesian coordinateCartesian**

are real numbers, these pairs are Cartesian coordinates of points in the Euclidean plane and thus form a subset of this plane, which is a curve in the case of a continuous function. In the simplest case one variable is plotted as a function of another, typically using rectangular axes; see Plot (graphics) for details.

A familiar example is the concept of the graph of a function.

### Section (fiber bundle)

**sectionsectionsLocal section**

There is a corresponding notion of a graph on a fibre bundle called a section.

A section is an abstract characterization of what it means to be a graph.

### Contour line

**isothermcontourscontour map**

It is a plane section of the three-dimensional graph of the function f(x, y) parallel to the (x, y)-plane.

### Convex function

**convexconvexitystrictly convex**

In mathematics, a real-valued function defined on an n-dimensional interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph.

### Chart

**chartsgraphgraphs**

A chart can represent tabular numeric data, functions or some kinds of qualitative structure and provides different info.

### Derivative

**differentiationdifferentiablefirst derivative**

The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.

### Surjective function

**surjectivesurjectiononto**

For example, to say that a function is onto (surjective) or not the codomain should be taken into account.

If (as is often done) a function is identified with its graph, then surjectivity is not a property of the function itself, but rather a property of the mapping.

### Concave function

**concaveconcavityconcave down**

1. A differentiable function f is (strictly) concave on an interval if and only if its derivative function f ′ is (strictly) monotonically decreasing on that interval, that is, a concave function has a non-increasing (decreasing) slope.

### Tetraview

A tetraview is an attempt to graph a complex function of a complex variable, by a method invented by Davide P. Cervone.

### Critical point (mathematics)

**critical pointcritical pointsdegenerate critical point**

These concepts may be visualized through the graph of f: at a critical point, the graph has a horizontal tangent if you can assign one at all.

### Stationary point

**stationarystationary pointsextremal**

In mathematics, particularly in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero.

### Y-intercept

**intercepty''-interceptintercepts**

In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.

### Epigraph (mathematics)

**epigraph**

In mathematics, the epigraph or supergraph of a function f : R n →R is the set of points lying on or above its graph:

### Asymptote

**asymptoticasymptoticallyasymptotes**

An important case is when the curve is the graph of a real function (a function of one real variable and returning real values).

### Vertical translation

**parallel shiftvertical displacement**

Often, vertical translations are considered for the graph of a function.

### Mathematics

**mathematicalmathmathematician**

In mathematics, the graph of a function

### Ordered pair

**ordered pairspairpairs**

is, formally, the set of all ordered pairs