The study of functions, graphing functions

Example.

  1. Scope
  2. Parity, odd parity, periodicity
  3. The function is neither even nor odd and periodic

  4. The intersection with the coordinate axes
  5. or

  6. The derivative and critical points
  7. or

  8. Intervals of increase, decrease, and extreme points (and the value of the function at these points)
  9. Дослідження функції

  10. The behavior of the functions at the ends of the scope and the asymptotes of the graph of a function (vertical, horizontal and inclined)

    Дослідження функції

    When you left

    In the case

    Therefore, vertical asymptote

    Since

    when then ie is the oblique asymptote

  11. The second derivative and the study of the function of the bulge and gnutt
  12. Find the inflection points (if they exist) and values in the points of inflection

    So the sign of the second derivative can change only at the point

    Дослідження функції

  13. If you want to find control points specifying the behavior of the graph
  14. Дослідження функції

  15. On the basis of the study building sketch the graph of a function
  16. Дослідження функції

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