Hyperbole – the schedule of the return proportionality of y=k/x where k - coefficient of the return proportionality is not equal to zero. Graphically the hyperbole is two smooth curved lines. Each of them specularly displays another concerning a point of the beginning of the Cartesian coordinates.

## It is required to you

- - pencil;
- - ruler.

## Instruction

1. Draw axes of coordinates. Put all necessary designations. If the y=k/x function, has k coefficient - bigger zero, then branches of a hyperbole will be placed in the first and third coordinate quarters. In this case function decreases on all range of definition which consists of two intervals: (-∞; 0) and (0; + ∞).

2. Construct at first a hyperbole branch on an interval (0; + ∞). Find the coordinates of points necessary for creation of a curve. For this purpose set variable x several any values and calculate values of variable y. For example, for the y=15/x function at x=45 we will receive y=1/3; at x=15, y=1; at x=5, y=3; at x=3, y=5; at x=1, y=15; at x=1/3, y=45. The more points you define, the graphic representation of the set function will turn out more precisely.

3. Apply the received points on the coordinate plane and connect them the smooth line. It will also be y=k/x function graph branch on an interval (0; + ∞). Pay attention that the curve never crosses axes of coordinates, and only infinitely gets closer to them since at x=0 the function is not defined.

4. Construct the second curve of a hyperbole on an interval (-∞; 0). For this purpose set variable x several any values from this numerical interval. Calculate values of variable y. So, for the y=-15/x function at x=-45 we will receive y=-1/3; at x=-15, y=-1; at x=-5, y=-3; at x=-3, y=-5; at x=-1, y=-15; at x=-1/3, y=-45.

5. Apply points on the coordinate plane. Connect them the smooth line. You received two symmetric curves concerning a point of intersection of axes of coordinates. The hyperbole is constructed.

6. If the y=k/x function, has k coefficient - smaller zero, then branches of a hyperbole will be placed in the second and fourth coordinate quarters. The function graph in this case increases, for example, for y=-15/x. It is under construction on the same algorithm, as a function graph with positive coefficient.