The study of a function is the task of determining the main parameters of a given function.
Content
Value
One of the goals of the study is to plot a function . Despite the fact that at present it is easy to do this by entering the function formula in the Google search query [1] , or by using numerous programs and devices, plotters , as well as more powerful systems of analytical calculations , the ability to examine the function on paper and plot the function by hand is still the same necessary element of mathematical education, as, for example, the ability to count and knowledge of the multiplication table .
Key Options
During the study, many parameters of the function as an object are found and written out in order. Here is the set from which they are usually selected:
- Domain of definition , behavior of a function near its boundary points
- The range of values (it is easier to find after studying the monotony), bounded above / below.
- Zeros (roots) of a function are points where it vanishes.
- Intervals of constancy of signs, signs in them.
- Parity / oddness , periodicity .
- Continuity
- If there are - break points, their types; vertical asymptotes .
- The first derivative , its zeros (critical points) or break points , if any.
- Extremums : highs and lows.
- Intervals of monotony
- The second derivative, its zeros.
- Inflection points , bulges .
- Behavior at infinity , horizontal or inclined asymptotes .
Sources
- Optional course in mathematics. 7-9 / Comp. I. L. Nikolskaya. - M .: Education , 1991 .-- S. 279-281. - 383 p. - ISBN 5-09-001287-3 .
See also
- Function graph