On the Internet it is not difficult to find calculators for plotting a function graph, which are brought to your attention in this review.
http://www.yotx.ru/
This service can build:
- ordinary graphs (like y = f(x)),
- specified parametrically,
- point graphs,
- graphs of functions in the polar coordinate system.
This online service V one step:
- Enter the function to be built
In addition to plotting a function graph, you will receive the result of studying the function.
Plotting function graphs:
http://matematikam.ru/calculate-online/grafik.php
You can enter manually or using the virtual keyboard at the bottom of the window. To enlarge the window with the graph, you can hide both the left column and the virtual keyboard.
Advantages of online charting:
- Visual display of entered functions
- Building very complex graphs
- Construction of graphs specified implicitly (for example, ellipse x^2/9+y^2/16=1)
- The ability to save charts and receive a link to them, which becomes available to everyone on the Internet
- Controlling scale and line color
- Possibility of plotting graphs by points, using constants
- Plotting several function graphs simultaneously
- Plotting in polar coordinates (use r and θ(\theta))
The service is in demand for finding intersection points of functions, for depicting graphs for further moving them into a Word document as illustrations when solving problems, and for analyzing the behavioral features of function graphs. The optimal browser for working with charts on this page of the site is Google Chrome. Correct operation is not guaranteed when using other browsers.
http://graph.reshish.ru/
You can build an interactive function graph online. Thanks to this, the graph can be scaled and moved around coordinate plane, which will allow you not only to receive general idea about the construction of this graph, but also to study in more detail the behavior of the function graph in sections.
To build a graph, select the function you need (on the left) and click on it, or enter it yourself in the input field and click ‘Build’. The argument is the variable 'x'.
To set a function nth root from 'x' use the notation x^(1/n) - pay attention to the parentheses: without them, following mathematical logic, you will get (x^1)/n.
You can omit the multiplication sign in expressions with numbers: 5x, 10sin(x), 3(x-1); between brackets:(x-7)(4+x); and also between the variable and brackets: x(x-3). Expressions like xsin(x) or xx will cause an error.
Consider the priority of operations and if you are not sure which will be executed first, add extra parentheses. For example: -x^2 and (-x)^2 are not the same thing.
Keep in mind that the graph may not be drawn if it tends to infinity in 'y' quickly enough, due to the inability of the computer to infinitely approach the asymptote in 'x'. This does not mean that the graph ends and does not continue indefinitely.
Trigonometric functions use radian angle units by default.
http://easyto.me/services/graphic/
In order to build several graphs in one coordinate system, check the box “Build in one coordinate system” and build graphs of functions one by one.
The service allows you to build graphs of functions that contain parameters.
To do this:
- Enter the function with parameters and click “Build graph”
- In the window that appears, choose which variable to plot against. Usually this is x.
- Change the settings in the History menu. The schedule will change before your eyes.
http://allcalc.ru/node/650
The service allows you to build graphs of functions in a rectangular coordinate system on a given range of values. In one coordinate plane, you can construct several graphs of functions at once.
To plot a function graph, you need to set the graph plotting area (for variable x and function y) and enter the value of the dependence of the function on the argument. It is possible to construct several graphs at the same time; to do this, you need to separate the functions using a semicolon. The graphs will be plotted on the same coordinate plane and will differ in color for clarity.
http://function-graph.ru/
To plot a function online, you just need to enter your function in a special field and click somewhere outside it. After this, the graph of the entered function will be drawn automatically.
If you need to plot several functions at the same time, then click on the blue “Add more” button. After this, another field will open in which you will need to enter the second function. Its schedule will also be built automatically.
You can adjust the color of the graph lines by clicking on the square located to the right of the function input field. The remaining settings are located directly above the graph area. With their help, you can set the background color, the presence and color of the grid, the presence and color of the axes, as well as the presence and color of the numbering of graph segments. If necessary, you can scale the function graph using the mouse wheel or special icons in the lower right corner of the drawing area.
After plotting the graph and making the necessary changes to the settings, you can download chart using the big green "Download" button at the very bottom. You will be prompted to save the function graph as a PNG image.
Unfortunately, not all students and schoolchildren know and love algebra, but everyone has to prepare homework, solve tests and take exams. Many people find it especially difficult to construct graphs of functions: if somewhere you don’t understand something, don’t finish learning it, or miss it, mistakes are inevitable. But who wants to get bad grades?
Would you like to join the cohort of students with tails and poor students? To do this, you have 2 ways: sit down with textbooks and fill in knowledge gaps, or use a virtual assistant - a service for automatically plotting function graphs according to given conditions. With or without a solution. Today we will introduce you to several of them.
The best thing about Desmos.com is its highly customizable interface, interactivity, the ability to organize results into tables and store your work in the resource database for free without time limits. The drawback is that the service is not fully translated into Russian.
Grafikus.ru
Grafikus.ru is another noteworthy Russian-language calculator for creating graphs. Moreover, he builds them not only in two-dimensional, but also in three-dimensional space.
Here is an incomplete list of tasks that this service successfully copes with:
- Drawing 2D graphs of simple functions: straight lines, parabolas, hyperbolas, trigonometric, logarithmic, etc.
- Drawing 2D graphs of parametric functions: circles, spirals, Lissajous figures and others.
- Drawing 2D graphs in polar coordinates.
- Construction of 3D surfaces of simple functions.
- Construction of 3D surfaces of parametric functions.
The finished result opens in a separate window. The user has the options of downloading, printing and copying a link to it. For the latter, you will have to log in to the service through the social network buttons.
The Grafikus.ru coordinate plane supports changing the boundaries of axes, their labels, grid spacing, as well as the width and height of the plane itself and font size.
The most strong point Grafikus.ru - the ability to create 3D graphs. Otherwise, it works no worse and no better than analogous resources.
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"Quadratic Function" - 1 Definition quadratic function 2 Properties of a function 3 Graphs of a function 4 Quadratic inequalities 5 Conclusion. Properties: Inequalities: Prepared by 8A class student Andrey Gerlitz. Plan: Graph: -Intervals of monotonicity for a > 0 for a< 0. Квадратичная функция. Квадратичные функции используются уже много лет.
“Quadratic function and its graph” - Solution.y=4x A(0.5:1) 1=1 A-belongs. When a=1, the formula y=ax takes the form.
“8th grade quadratic function” - 1) Construct the vertex of a parabola. Plotting a graph of a quadratic function. x. -7. Construct a graph of the function. Algebra 8th grade Teacher 496 Bovina school T.V. -1. Construction plan. 2) Construct the axis of symmetry x=-1. y.
Constructing graphs of functions containing modules usually causes considerable difficulties for schoolchildren. However, everything is not so bad. It is enough to remember a few algorithms for solving such problems, and you can easily build a graph even for the most seemingly complex function. Let's figure out what kind of algorithms these are.
1. Plotting a graph of the function y = |f(x)|
Note that the set of function values y = |f(x)| : y ≥ 0. Thus, the graphs of such functions are always located entirely in the upper half-plane.
Plotting a graph of the function y = |f(x)| consists of the following simple four steps.
1) Carefully and carefully construct a graph of the function y = f(x).
2) Leave unchanged all points on the graph that are above or on the 0x axis.
3) Display the part of the graph that lies below the 0x axis symmetrically relative to the 0x axis.
Example 1. Draw a graph of the function y = |x 2 – 4x + 3|
1) We build a graph of the function y = x 2 – 4x + 3. Obviously, the graph of this function is a parabola. Let's find the coordinates of all points of intersection of the parabola with the coordinate axes and the coordinates of the vertex of the parabola.
x 2 – 4x + 3 = 0.
x 1 = 3, x 2 = 1.
Therefore, the parabola intersects the 0x axis at points (3, 0) and (1, 0).
y = 0 2 – 4 0 + 3 = 3.
Therefore, the parabola intersects the 0y axis at the point (0, 3).
Parabola vertex coordinates:
x in = -(-4/2) = 2, y in = 2 2 – 4 2 + 3 = -1.
Therefore, point (2, -1) is the vertex of this parabola.
Draw a parabola using the data obtained (Fig. 1)
2) The part of the graph lying below the 0x axis is displayed symmetrically relative to the 0x axis.
3) We get a graph of the original function ( rice. 2, shown in dotted line).
2. Plotting the function y = f(|x|)
Note that functions of the form y = f(|x|) are even:
y(-x) = f(|-x|) = f(|x|) = y(x). This means that the graphs of such functions are symmetrical about the 0y axis.
Plotting a graph of the function y = f(|x|) consists of the following simple chain of actions.
1) Graph the function y = f(x).
2) Leave that part of the graph for which x ≥ 0, that is, the part of the graph located in the right half-plane.
3) Display the part of the graph specified in point (2) symmetrically to the 0y axis.
4) As the final graph, select the union of the curves obtained in points (2) and (3).
Example 2. Draw a graph of the function y = x 2 – 4 · |x| + 3
Since x 2 = |x| 2, then the original function can be rewritten in the following form: y = |x| 2 – 4 · |x| + 3. Now we can apply the algorithm proposed above.
1) We carefully and carefully build a graph of the function y = x 2 – 4 x + 3 (see also rice. 1).
2) We leave that part of the graph for which x ≥ 0, that is, the part of the graph located in the right half-plane.
3) Display the right side of the graph symmetrically to the 0y axis.
(Fig. 3).
Example 3. Draw a graph of the function y = log 2 |x|
We apply the scheme given above.
1) Build a graph of the function y = log 2 x (Fig. 4).
3. Plotting the function y = |f(|x|)|
Note that functions of the form y = |f(|x|)| are also even. Indeed, y(-x) = y = |f(|-x|)| = y = |f(|x|)| = y(x), and therefore, their graphs are symmetrical about the 0y axis. The set of values of such functions: y ≥ 0. This means that the graphs of such functions are located entirely in the upper half-plane.
To plot the function y = |f(|x|)|, you need to:
1) Carefully construct a graph of the function y = f(|x|).
2) Leave unchanged the part of the graph that is above or on the 0x axis.
3) Display the part of the graph located below the 0x axis symmetrically relative to the 0x axis.
4) As the final graph, select the union of the curves obtained in points (2) and (3).
Example 4. Draw a graph of the function y = |-x 2 + 2|x| – 1|.
1) Note that x 2 = |x| 2. This means that instead of the original function y = -x 2 + 2|x| – 1
you can use the function y = -|x| 2 + 2|x| – 1, since their graphs coincide.
We build a graph y = -|x| 2 + 2|x| – 1. For this we use algorithm 2.
a) Graph the function y = -x 2 + 2x – 1 (Fig. 6).
b) We leave that part of the graph that is located in the right half-plane.
c) We display the resulting part of the graph symmetrically to the 0y axis.
d) The resulting graph is shown in the dotted line in the figure (Fig. 7).
2) There are no points above the 0x axis; we leave the points on the 0x axis unchanged.
3) The part of the graph located below the 0x axis is displayed symmetrically relative to 0x.
4) The resulting graph is shown in the figure with a dotted line (Fig. 8).
Example 5. Graph the function y = |(2|x| – 4) / (|x| + 3)|
1) First you need to plot the function y = (2|x| – 4) / (|x| + 3). To do this, we return to Algorithm 2.
a) Carefully plot the function y = (2x – 4) / (x + 3) (Fig. 9).
Note that this function is fractional linear and its graph is a hyperbola. To plot a curve, you first need to find the asymptotes of the graph. Horizontal – y = 2/1 (the ratio of the coefficients of x in the numerator and denominator of the fraction), vertical – x = -3.
2) We will leave that part of the graph that is above the 0x axis or on it unchanged.
3) The part of the graph located below the 0x axis will be displayed symmetrically relative to 0x.
4) The final graph is shown in the figure (Fig. 11).
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