graph

(noun)

A diagram displaying data; in particular one showing the relationship between two or more quantities, measurements or indicative numbers that may or may not have a specific mathematical formula relating them to each other.

Related Terms

  • proprietary
  • scientific calculator

Examples of graph in the following topics:

  • Graphing on Computers and Calculators

    • They can be created with graphing calculators.
    • Graphs are often created using computer software.
    • GraphCalc includes many of the standard features of graphing calculators, but also includes some higher-end features.
    • c) Three-dimensional graphing: While high-end graphing calculators can graph in 3-D, GraphCalc benefits from modern computers' memory, speed, and graphics acceleration.
    • It also includes tools for visualizing and analyzing graphs.
  • Real Numbers, Functions, and Graphs

    • Graphs can be used to represent these relationships pictorially.
    • The graph of a function $f$ is the collection of all ordered pairs $(x, f(x))$.
    • Graphing on a Cartesian plane is sometimes referred to as curve sketching.
    • If the function input $x$ is an ordered pair $(x_1, x_2)$ of real numbers, the graph is the collection of all ordered triples $(x_1, x_2, f(x_1, x_2))$ and its graphical representation is a surface (see the three-dimensional graph below).
    • This is a graph of the function $f(x,y) = \sin{x^2} \cos{y^2}$
  • Using Calculators and Computers

    • For numerical calculations and graphing, scientific calculators and personal computers are commonly used in classes and laboratories.
    • In certain contexts such as higher education, scientific calculators have been superseded by graphing calculators , which offer a superset of scientific calculator functionality along with the ability to graph input data and write and store programs for the device.
    • These days, scientific and graphing calculators are often replaced by personal computers or even by supercomputers.
    • A typical graphing calculator built by Texas Instruments, displaying a graph of a function $f(x)=2x^2-3$.
    • Describe how calculators and computers can assist with arithmetic, graphing, and other complicated operations.
  • Derivatives and the Shape of the Graph

    • The shape of a graph may be found by taking derivatives to tell you the slope and concavity.
    • If $x$ and y are real numbers, and if the graph of $y$ is plotted against $x$, the derivative measures the slope of this graph at each point.
    • The simplest case is when $y$ is a linear function of $x$, meaning that the graph of $y$ divided by $x$ is a straight line.
    • If the function $f$ is not linear (i.e. its graph is not a straight line), however, then the change in $y$ divided by the change in $x$ varies: differentiation is a method to find an exact value for this rate of change at any given value of $x$.
    • Sketch the shape of a graph by using differentiation to find the slope and concavity
  • Linear and Quadratic Functions

    • Linear and quadratic functions make lines and a parabola, respectively, when graphed and are some of the simplest functional forms.
    • Linear and quadratic functions make lines and parabola, respectively, when graphed.
    • Although affine functions make lines when graphed, they do not satisfy the properties of linearity.
    • The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y-axis .
  • Vector-Valued Functions

    • The graph shows a visual representation of
    • If you were to take a cross section, with the cut perpendicular to any of the three axes, you would see the graph of that function.
    • For example, if you were to slice the three-dimensional shape perpendicular to the $z$-axis, the graph you would see would be of the function $z(t)=t$.The domain of a vector valued function is a domain that satisfies all of the component functions.
    • This a graph of a parametric curve (a simple vector-valued function with a single parameter of dimension $1$).
    • The graph is of the curve: $\langle 2 \cos(t), 4 \sin(t),t \rangle$ where $t$ goes from $0$ to $8 \pi$.
  • Derivatives and Rates of Change

    • The simplest case is when $y$ is a linear function of x, meaning that the graph of $y$ divided by $x$ is a straight line.
    • If the function $f$ is not linear (i.e., its graph is not a straight line), however, then the change in $y$ divided by the change in $x$ varies: differentiation is a method to find an exact value for this rate of change at any given value of $x$.
    • If $x$ and $y$ are real numbers, and if the graph of $y$ is plotted against $x$, the derivative measures the slope of this graph at each point.
    • Describe the derivative as the change in $y$ over the change in $x$ at each point on a graph
  • Area Between Curves

    • The area between the graphs of two functions is equal to the integral of a function, $f(x)$, minus the integral of the other function, $g(x)$: $A = \int_a^{b} ( f(x) - g(x) ) \, dx$.
    • The area between the graphs of two functions is equal to the integral of one function, $f(x)$, minus the integral of the other function, $g(x)$: A=∫ba(f(x)−g(x))dxA = \int_a^{b} ( f(x) - g(x) ) \, dx where $f(x)$ is the curve with the greater y-value .
    • The area between two graphs can be evaluated by calculating the difference between the integrals of the two functions.
  • Derivatives of Exponential Functions

    • The slope of the graph at any point is the height of the function at that point.
    • Graph of the exponential function illustrating that its derivative is equal to the value of the function.
  • Inverse Trigonometric Functions: Differentiation and Integration

    • The usual principal values of the $\text{arctan}(x)$ and $\text{arccot}(x)$ functions graphed on the Cartesian plane.
    • Principal values of the $\text{arcsec}(x)$ and $\text{arccsc}(x)$ functions graphed on the Cartesian plane.
    • The usual principal values of the $\arcsin(x)$ and $\arccos(x)$ functions graphed on the Cartesian plane.
Subjects
  • Accounting
  • Algebra
  • Art History
  • Biology
  • Business
  • Calculus
  • Chemistry
  • Communications
  • Economics
  • Finance
  • Management
  • Marketing
  • Microbiology
  • Physics
  • Physiology
  • Political Science
  • Psychology
  • Sociology
  • Statistics
  • U.S. History
  • World History
  • Writing

Except where noted, content and user contributions on this site are licensed under CC BY-SA 4.0 with attribution required.