In elementary and higher mathematics such term as a hyperbole meets. So call a function graph which does not pass through the beginning of coordinates and represents two curves parallel each other. There are several ways of creation of a hyperbole.
Instruction
1. The hyperbole as well as other curves can be constructed in two ways. The first of them consists in construction on a rectangle, and the second - on a function graph of f (x) =k/x. To begin to build a hyperbole follows from creation of a rectangle from the ends on axis x called A1 and A2 and with the opposite ends on axis y called B1 and B2. Carry out a rectangle through the center of coordinates, as shown in figure 1. The parties have to be parallel and equal in size both A1A2, and B1B2. Through the center of a rectangle, i.e. the beginning of coordinates, carry out two diagonals. Having drawn these diagonals, you receive two straight lines which are schedule asymptotes. Construct one branch of a hyperbole, and then, the same way, and opposite. Function is increasing on an interval [a; ∞]. Therefore its asymptotes will be: y=bx/a; y=-bx/a. The equation of a hyperbole will take a form: y = √ x^2-a^2
2. If instead of a rectangle to use a square, the equilateral hyperbole, as in figure 2 will turn out. Its initial equation has an appearance: x^2-y^2=a^2У of an equilateral hyperbole of an asymptote are perpendicular each other. Besides, between y and x there is a proportional dependence which is that if x to reduce in the set number of times, then y will increase in as much time and vice versa. Therefore, in a different way the equation of a hyperbole registers in a look: y=k/x
3. If in a condition function f (x) =k/x is given, then it is more expedient to build a hyperbole on points. Considering that k is a constant, and x≠0 denominator, it is possible to come to a conclusion that the function graph does not pass through the beginning of coordinates. Respectively, intervals of function are equal (-∞; 0) and (0; ∞) as at the address x to zero the function loses the meaning. At increase x the f (x) function decreases, and at reduction increases. At approach x to zero y condition →∞ is met. The function graph is shown in the main drawing.
4. For creation of a hyperbole by method of calculation it is convenient to use the calculator. If he is capable to work according to the program or at least to remember formulas, it is possible to force it to perform calculation several times (on number of points), without gathering expression every time anew. Even more conveniently in this sense the graphic calculator which will undertake, besides calculation, and creation of the schedule.