How to find a function with the graphics

In school we studied in detail the functions and construct their graphs. However, to read the graph of the function and find its kind on the finished drawing, we are, unfortunately, practically is not taught. In fact, it is not difficult if you remember a few basic types of functions.The task of describing the properties of a function from its schedule often arises in experimental studies. For graphics , you can determine the intervals of increasing and decreasing functions, discontinuities and extrema, and also you can see the asymptotes.

Instruction

1. If the graph is a straight line passing through the origin and forming with the axis OX the angle α (the angle of inclination of a straight line to the positive half-axis OX). The function that describes this line will have the form y = kx. The coefficient of proportionality k is equal to tg α. If the line passes through 2 nd and 4-th quadrant, k < 0, and the function is decreasing if in the 1st and 3rd, then k > 0 and a function increases.Let the graph is a straight line, arranged in different ways relative to the axes of coordinates. It is a linear function, and it has the form y = kx + b, where variables x and y are in the first degree, and k and b can take both positive and negative values or zero. Video is parallel to the line y = kx cuts and on the y-axis |b| units. A line parallel to the x-axis, then k = 0 if the y-axis, the equation has the form x = const.
2. A curve consisting of two branches, located in different quarters and symmetric about the origin, is called a hyperbola. This graph expresses the inverse relationship of the variable y from x and is described by the equation y = k/x. Here k ≠ 0 is the coefficient of inverse proportionality. In this case, if k > 0, the function decreases; if k < 0 the function is increasing. Thus, the domain of the function is the entire number line except x = 0. The branches of the hyperbola approach the coordinate axes as their asymptotes. With decreasing k the branches of the hyperbola are more "pressed" into the coordinate angles.
3. A quadratic function has the form y = ax2 + bx + C, where a, b and c values constant and a  0. If the condition b = C = 0, a function equation looks like y = ax2 (the simplest case of a quadratic function), and its graph is a parabola passing through the origin. The graph of the function y = ax2 + bx + C has the same form as the simplest case of functions, however, its peak (the point of intersection of the parabola with the axis OY) lies not in the origin.
4. A parabola is also the graph of the exponential function expressed by the equation y = xⁿ, if n is any even number. If n is any odd number, the graph of this exponential function will have the form of a cubic parabola.
   If n is any negative number, a function equation takes the form. The graph of the function with odd n is a hyperbola, and if n is even their branches are symmetric about the axis Oy.