Into the golden age information technologies few people will buy graph paper and spend hours drawing a function or an arbitrary set of data, and why bother with such tedious work when you can plot a function graph online. In addition, counting millions of expression values ​​for correct display is almost unrealistic and difficult, and despite all efforts, the result will be a broken line, not a curve. Therefore, in this case, the computer is an indispensable assistant.

What is a function graph

A function is a rule according to which each element of one set is associated with some element of another set, for example, the expression y = 2x + 1 establishes a connection between the sets of all values ​​of x and all values ​​of y, therefore, this is a function. Accordingly, the graph of a function will be the set of points whose coordinates satisfy the given expression.

In the figure we see the graph of the function y = x. This is a straight line and each of its points has its own coordinates on the axis X and on the axis Y. Based on the definition, if we substitute the coordinate X some point into this equation, then we get the coordinate of this point on the axis Y.

Online services for plotting function graphs

Let's look at several popular and best services that allow you to quickly draw a graph of a function.

The list opens with the most common service that allows you to plot a function graph using an equation online. Umath contains only the necessary tools, such as scaling, moving along the coordinate plane and viewing the coordinates of the point at which the mouse is pointing.

Instructions:

1. Enter your equation in the field after the "=" sign.
2. Click the button "Build a graph".

As you can see, everything is extremely simple and accessible; the syntax for writing complex mathematical functions: with modulus, trigonometric, exponential - is given right below the graph. Also, if necessary, you can set the equation using the parametric method or build graphs in the polar coordinate system.

Yotx has all the functions of the previous service, but at the same time it contains such interesting innovations as creating a function display interval, the ability to build a graph using tabular data, and also display a table with entire solutions.

Instructions:

1. Select the desired method for setting the schedule.
2. Enter your equation.
3. Set the interval.
4. Click the button "Build".

For those who are too lazy to figure out how to write down certain functions, this position offers a service with the ability to select the one you need from a list with one click of the mouse.

Instructions:

1. Find the function you need from the list.
2. Left click on it
3. If necessary, enter coefficients in the field "Function:".
4. Click the button "Build".

In terms of visualization, it is possible to change the color of the graph, as well as hide it or delete it altogether.

Desmos is by far the most sophisticated service for constructing equations online. By moving the cursor with the left mouse button held down along the graph, you can view in detail all the solutions to the equation with an accuracy of 0.001. The built-in keyboard allows you to quickly write powers and fractions. The most important advantage is the ability to write the equation in any state without reducing it to the form: y = f(x).

Instructions:

1. In the left column, right-click on an empty line.
2. In the lower left corner, click on the keyboard icon.
3. In the panel that appears, enter the required equation (to write the names of functions, go to the “A B C” section).
4. The schedule is built in real time.

The visualization is simply perfect, adaptive, it’s clear that designers worked on the application. On the plus side, we can note the huge abundance of possibilities, for mastering which you can see examples in the menu in the upper left corner.

There are a great many sites for constructing function graphs, but everyone is free to choose for themselves based on the required functionality and personal preferences. The list of the best was compiled to satisfy the requirements of any mathematician, young or old. Good luck to you in comprehending the “queen of sciences”!

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 tail-seekers and losers? 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 - another one worthy of attention Russian-language calculator for plotting graphs. Moreover, he builds them not only in two dimensions, 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 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 greatest strength of Grafikus.ru is the ability to create 3D graphics. Otherwise, it works no worse and no better than analogue resources.

Onlinecharts.ru

The online assistant Onlinecharts.ru builds not graphs, but diagrams of almost all existing types. Including:

• Linear.
• Columnar.
• Circular.
• With regions.
• Radial.
• XY-graphs.
• Bubble.
• Spot.
• Polar bubbles.
• Pyramids.
• Speedometers.
• Columnar-linear.

Using the resource is very simple. Appearance diagrams (background color, grid, lines, pointers, corner shapes, fonts, transparency, special effects, etc.) are completely user defined. Data for construction can be entered either manually or imported from a table in a CSV file stored on a computer. The finished result is available for downloading to a PC in the form of an image, PDF, CSV or SVG file, as well as for saving online on the ImageShack.Us photo hosting site or in personal account Onlinecharts.ru. The first option can be used by everyone, the second - only registered ones.

A function graph is a visual representation of the behavior of a function on a coordinate plane. Graphs help you understand various aspects of a function that cannot be determined from the function itself. You can build graphs of many functions, and each of them will be given a specific formula. The graph of any function is built using a specific algorithm (if you have forgotten the exact process of graphing a specific function).

Steps

Graphing a Linear Function

Determine whether the function is linear. The linear function is given by a formula of the form F (x) = k x + b (\displaystyle F(x)=kx+b) or y = k x + b (\displaystyle y=kx+b)(for example, ), and its graph is a straight line. Thus, the formula includes one variable and one constant (constant) without any exponents, root signs, or the like. If a function of a similar type is given, it is quite simple to plot a graph of such a function. Here are other examples of linear functions:

Use a constant to mark a point on the Y axis. The constant (b) is the “y” coordinate of the point where the graph intersects the Y axis. That is, it is a point whose “x” coordinate is equal to 0. Thus, if x = 0 is substituted into the formula, then y = b (constant). In our example y = 2 x + 5 (\displaystyle y=2x+5) the constant is equal to 5, that is, the point of intersection with the Y axis has coordinates (0.5). Place this point on coordinate plane.

Find slope straight. It is equal to the multiplier of the variable. In our example y = 2 x + 5 (\displaystyle y=2x+5) with the variable “x” there is a factor of 2; thus, the slope coefficient is equal to 2. The slope coefficient determines the angle of inclination of the straight line to the X axis, that is, the greater the slope coefficient, the faster the function increases or decreases.

Write the slope as a fraction. The angular coefficient is equal to the tangent of the angle of inclination, that is, the ratio of the vertical distance (between two points on a straight line) to the horizontal distance (between the same points). In our example, the slope is 2, so we can state that the vertical distance is 2 and the horizontal distance is 1. Write this as a fraction: 2 1 (\displaystyle (\frac (2)(1))).

• If the slope is negative, the function is decreasing.

1. From the point where the straight line intersects the Y axis, plot a second point using vertical and horizontal distances. Schedule linear function can be constructed from two points. In our example, the intersection point with the Y axis has coordinates (0.5); From this point, move 2 spaces up and then 1 space to the right. Mark a point; it will have coordinates (1,7). Now you can draw a straight line.

   Using a ruler, draw a straight line through two points. To avoid mistakes, find the third point, but in most cases the graph can be plotted using two points. Thus, you have plotted a linear function.

   Plotting points on the coordinate plane

   1. Define a function. The function is denoted as f(x). All possible values ​​of the variable "y" are called the domain of the function, and all possible values ​​of the variable "x" are called the domain of the function. For example, consider the function y = x+2, namely f(x) = x+2.

      Draw two intersecting perpendicular lines. The horizontal line is the X axis. The vertical line is the Y axis.

      Label the coordinate axes. Divide each axis into equal segments and number them. The intersection point of the axes is 0. For the X axis: positive numbers are plotted to the right (from 0), and negative numbers to the left. For the Y axis: positive numbers are plotted on top (from 0), and negative numbers on the bottom.

      Find the values ​​of "y" from the values ​​of "x". In our example, f(x) = x+2. Substitute specific x values ​​into this formula to calculate the corresponding y values. If given a complex function, simplify it by isolating the “y” on one side of the equation.

      • -1: -1 + 2 = 1
      • 0: 0 +2 = 2
      • 1: 1 + 2 = 3

   2. Plot the points on the coordinate plane. For each pair of coordinates, do the following: find the corresponding value on the X axis and draw a vertical line (dotted); find the corresponding value on the Y axis and draw a horizontal line (dashed line). Mark the intersection point of the two dotted lines; thus, you have plotted a point on the graph.

      Erase the dotted lines. Do this after plotting all the points on the graph on the coordinate plane. Note: the graph of the function f(x) = x is a straight line passing through the coordinate center [point with coordinates (0,0)]; the graph f(x) = x + 2 is a line parallel to the line f(x) = x, but shifted upward by two units and therefore passing through the point with coordinates (0,2) (because the constant is 2).

   Graphing a Complex Function

   Find the zeros of the function. The zeros of a function are the values ​​of the x variable where y = 0, that is, these are the points where the graph intersects the X-axis. Keep in mind that not all functions have zeros, but they are the first step in the process of graphing any function. To find the zeros of a function, equate it to zero. For example:

   Find and mark the horizontal asymptotes. An asymptote is a line that the graph of a function approaches but never intersects (that is, in this region the function is not defined, for example, when dividing by 0). Mark the asymptote with a dotted line. If the variable "x" is in the denominator of a fraction (for example, y = 1 4 − x 2 (\displaystyle y=(\frac (1)(4-x^(2))))), set the denominator to zero and find “x”. In the obtained values ​​of the variable “x” the function is not defined (in our example, draw dotted lines through x = 2 and x = -2), because you cannot divide by 0. But asymptotes exist not only in cases where the function contains fractional expression. Therefore, it is recommended to use common sense:

“Natural logarithm” - 0.1. Natural logarithms. 4. Logarithmic darts. 0.04. 7.121.

“Power function grade 9” - U. Cubic parabola. Y = x3. 9th grade teacher Ladoshkina I.A. Y = x2. Hyperbola. 0. Y = xn, y = x-n where n is the given natural number. X. The exponent is an even natural number (2n).

"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.