Operations of superposition and closure. Completeness, basis of a system of functions

Build a function

We bring to your attention a service for plotting function graphs online, all rights to which belong to the company Desmos. Use the left column to enter functions. You can enter it manually or with virtual keyboard at the bottom of the window. To enlarge the chart window, you can hide both the left column and the virtual keyboard.

Benefits of online charting

  • Visual display of introduced functions
  • Building very complex graphs
  • Plotting implicitly defined graphs (e.g. ellipse x^2/9+y^2/16=1)
  • The ability to save charts and get a link to them, which becomes available to everyone on the Internet
  • Scale control, line color
  • The ability to plot graphs by points, the use of constants
  • Construction of several graphs of functions at the same time
  • Plotting in polar coordinates (use r and θ(\theta))

With us it is easy to build graphs of varying complexity online. The construction is done instantly. The service is in demand for finding intersection points of functions, for displaying graphs for their further movement to word document as illustrations in solving problems, for analyzing the behavioral features of function graphs. The optimal browser for working with charts on this page of the site is Google Chrome. When using other browsers, correct operation is not guaranteed.

Correspondence G between sets A And IN called a subset. If , then they say that b

corresponds A. The set of all matching elements

called way element a. The set of all that an element corresponds to is called

prototype element b.

Plenty of couples (b, a) such as is called reverse

towards G and is denoted. The concepts of image and prototype for

" G and are mutually inverse.

Examples. 1) Let's put in correspondence with a natural number P

set of real numbers . The image of the number 5

there will be a half-interval

(this is the largest integer less than or equal to X). The preimage of the number 5 in this correspondence is an infinite set: half-interval)

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