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HOW explore function

How to explore the function

The study called special functionsjob in the school course of mathematics, during which identifies the main parameters of the function and its graph is constructed. Previously, the purpose of this study was plotting, but today this problem is solved with the help of specialized software.

Still, no harm will be familiar with the general scheme of the research function.



Located domain of the function, ie, range of values ​​x, in which the function takes any value.


Defines the area of ​​continuity and discontinuity point. It is usually the continuity of the field coincides with the domain of the function, it is necessary to explore the left and right side-chapels isolated points.


Checks for vertical asymptote. If the function has discontinuities, it is necessary to investigate the ends of the respective periods.


The parity and odd function is checked by definition. The function y = f (x) is called even if for any x in the domain of the equality f (-x) = f (x).


Function checked at intervals. To do this, x is changed to x + T and sought the smallest positive number T. If there is a number, the function is periodic, and the integer T - the period of the function.


Function tested for monotony, areextremum point. This equates to a derivative of zero, found at this point, put on a number line and added to them the points at which the derivative is not defined. Signs of the derivative on the resulting intervals determined by the area of ​​monotony, as the transition point between the different areas are extremes of functions.


We study the convexity of the function, there are inflection points. Research is carried out similar studies in the monotony, but it is considered the second derivative.


Are points of intersection with the axes OX and OY, wherein y = f (0) - with the intersection of axis OY, f (x) = 0 - intersection with axis OX.


Defines the limits at the ends of the field definition.


Plot functions.


According to the schedule determined by the range of the function and limited functions.

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