One of widespread ways of studying functions – creation of their schedules. However, knowing the main properties of graphic display of functions, it is possible to calculate a formula according to the schedule.
Instruction
1. It is the simplest to calculate a straight line formula, in a general view it corresponds to the equation at =kx+b. Find coordinates of any two points belonging to a straight line and set up them in the equation (an abscissa instead of x, ordinate instead of s). At you the system from two equations, having solved which will turn out, you will find coefficients of k and b. Having substituted values in a general view of the equation, you will see the formula corresponding to yoursto to the schedule.
2. Look how schedules of standard square functions look, and compare them to the drawing. If the schedule is symmetric concerning any line and a form reminds a parabola or a hyperbole, three points will be necessary for you for determination of coefficients of the equation. For example, the parabola equation in a general view looks as at =ax^2+bx+c. Having substituted values of three points and having received a system from three equations, you will be able to find coefficients of a, b, c.
3. If the schedule is similar to a sinusoid or a cosinusoid, try to find the equation the following method. Define as far as the schedule differs from standard. If it is compressed on ordinate axis in n of times, so in the equation the sign sin or cos there is a multiplier less than unit (if it is stretched on an axis ou, then the multiplier is more than unit).
4. If the schedule is stretched or compressed on an axis oh, draw a conclusion that before a variable in trigonometrical function there is a number (if number more than 1, the schedule is compressed if less than 1 – stretch).
5. At construction of trigonometrical function in degree its schedule becomes or more flat (at degree less than 1), or more abrupt (at degree more than 1). Besides, at construction in even degree a part of the schedule will be lower than an axis oh is symmetrically displayed up.
6. The schedule can be simply postponed up or down for some distance. In that case add to value of function it is number, for example, at =tgx+2. If the schedule is transferred to the left or to the right, add number to value of an argument, for example, of y=tg (x + O).