Tip 1: How to build a feature
Tip 1: How to build a feature
A function is a mathematical expression in whichThe dependence of one variable on another is determined or the relationship between the elements of different sets is reflected. In this case, one meaning of the set corresponds to a certain value of the other. Usually, the function is given by an equation, by solving which, it is possible to determine the range of its value-those values of the variable at which the algebraic equation makes sense.
Instructions
1
The equation is written in the form of a formula in the leftpart of which is the required value of y, and on the right side - the expression in which it is necessary to find the value of the variable x. The graph of a function is usually constructed in a rectangular coordinate system. The equation defines the name of the function. The linear function, for example, is determined by the equation of the simple dependence of y on x. The graph of such a function is a straight line. A parabola is a graphical solution of the quadratic equation. Trigonometric functions in a graphic representation are calculated curves.
2
To plot the function graph. Specify the numerical values of the variable x, get the values of the desired y, write the results to a table, where each x will correspond to a certain y.
3
Build on a sheet of paper in millimeters orpage in the cell coordinate system, which is formed by intersecting horizontal and vertical lines. Specify the abscissa x (horizontal line) and the ordinate y (vertical line), mark the intersection point O - the origin. Select on each axis a positive direction, specify it with arrows (on the abscissa - to the right, on the ordinate - upwards), set the units of measurement, indicating equal segments in figures in order.
4
In accordance with the created table, find the points on the coordinate plane, the coordinates of which will satisfy the conditions of the equation. Mark the dots with letters or numbers.
5
Connect the found points by a continuous line. If the value of the variable x or y is 0, then the graph will intersect the coordinate axes. If there is a constant value of n in the equation, the graph will be shifted by n units relative to the coordinate axes.
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The skills of the study of functions and the construction of graphs are now taught in the 8th grade of the secondary school. However, with the complication of functions, their solutions, the construction of graphs becomes more complicated.
7
There are many computer programs,allowing you to build various graphics of the most complex functions. But the elementary knowledge in the decision of functions and construction of their schedules is necessary for each student.
Tip 2: How to construct a quadratic function
The function, which is given by the formula f (x) = ax² +bx + c, where a ≠ 0 is called a quadratic function. The number D, calculated by the formula D = b² - 4ac, is called the discriminant and determines the set of properties of the quadratic function. The graph of this function is the parabola, its location on the plane, and hence the number of roots of the equation depends on the discriminant and the coefficient a.
Instructions
1
For values of D> 0 and a> 0, the graph of the functionis directed upwards and has two points of intersection with the x axis, so the equation has two roots. Point B indicates the vertex of the parabola, its coordinates are calculated by the formulas x = -b / 2 * a; y = c - b? / 4 * a. Point A is the intersection with the y axis, its coordinates are x = 0; y = c.
2
If D = 0 and a> 0, then the parabola is also directed upward, but has one point of tangency with the abscissa, so there is only one solution of the equation.
3
For D <0 and a> 0, the equation has no roots, since the graph does not intersect the x-axis, and its branches are directed upwards.
4
In the case when D> 0 and a <0, the branches of the parabola are directed downward, and the equation has two roots.
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If D = 0 and a <0, the equation has one solution, while the graph of the function is directed downward and has one point of tangency with the abscissa axis.
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Finally, if D <0 and a <0, then the equation does not have solutions, since the graph does not intersect the x axis.
Tip 3: How to build a linear function
In elementary mathematics, the function is calleddefinite dependence of one parameter on the other. Functions are linear and nonlinear. The graph of a linear function is a straight line, a nonlinear curve is a curve each of whose sections has a different slope.
You will need
- - calculator,
- - a pencil,
- - millimeter paper,
- - ruler.
Instructions
1
The linear function has the form: C = Ax + Bygde A, B and C are some numerical values. That is, changing the argument x entails a proportional change in the function y. On the graph this looks like a straight line passing through "0", if "C" is zero; a straight line parallel to the abscissa axis, if "A" is zero; and a straight line parallel to the ordinate axis, if "B" is zero. In the event that "A" or "B" is zero, the function takes the form of a constant.
2
Give the equation of the function in a form convenient forplotting its graph: y = A / Bx + C / B, where A / B is the slope, which characterizes the slope of the graph of the linear function. It is equal to the tangent of the angle between the straight line of the graph of the linear dependence and the axis of abscissas - the angle is measured upwards from the X axis. Depending on whether the positive value of the angular coefficient is negative or negative, this angle is acute or obtuse. In case the value of "C" is zero, takes the form: y = A / Bx The function of this kind is called direct proportionality.
3
Substitute in the equation of the function y some value of the argument x. Set this x to the abscissa.
4
Calculate the value of the function on the ordinate axis, drawn on millimeter paper.
5
Swipe with the ruler, from thethe axis of abscissas of the value of the argument is vertical until it intersects with the horizontal drawn from the value of the function set on the ordinate axis. The intersection of these lines is the first point of the graph of a linear function. We call it the point D.
6
Repeat for the other value of the argument.
7
Find the second point of the graph of the linear function, plotting the corresponding values of x and y on the abscissa and ordinate axes. Let this be the point F.
8
Pass through the points D and F a straight line. This is the graph of our linear function. The construction is finished.
