Mister Exam

Curve tracing functions Step by Step


Graph Limits:

from to

Intersection points:

does show?


    What studies?

    • The domain of the function. It can only determine the points at which the denominator of the function equal to zero
    • It can determine the intersection points of the function graph with the coordinate axes
    • Extremes of the function: intervals (segments) of increasing and decreasing of the function, as well as local (or relative) and global (or absolute) minima and maxima of the function (minimum, maximum, the minimum and maximum values of the function)
    • Inflection points of the function graph: inflection points: intervals of convexity, concavity (convexity)
    • Vertical asymptotes: the domain of the function definition, the points where the denominator of the function equal to zero
    • The horizontal asymptote of the graph of the function
    • The oblique asymptote of the graph of a function
    • Even and odd functions

    Examples of functions

    Learn more about Curve sketching.

    The above examples also contain:

    • the modulus or absolute value: absolute(x) or |x|
    • square roots sqrt(x),
      cubic roots cbrt(x)
    • trigonometric functions:
      sinus sin(x), cosine cos(x), tangent tan(x), cotangent ctan(x)
    • exponential functions and exponents exp(x)
    • inverse trigonometric functions:
      arcsine asin(x), arccosine acos(x), arctangent atan(x), arccotangent acot(x)
    • natural logarithms ln(x),
      decimal logarithms log(x)
    • hyperbolic functions:
      hyperbolic sine sh(x), hyperbolic cosine ch(x), hyperbolic tangent and cotangent tanh(x), ctanh(x)
    • inverse hyperbolic functions:
      hyperbolic arcsine asinh(x), hyperbolic arccosinus acosh(x), hyperbolic arctangent atanh(x), hyperbolic arccotangent acoth(x)
    • other trigonometry and hyperbolic functions:
      secant sec(x), cosecant csc(x), arcsecant asec(x), arccosecant acsc(x), hyperbolic secant sech(x), hyperbolic cosecant csch(x), hyperbolic arcsecant asech(x), hyperbolic arccosecant acsch(x)
    • rounding functions:
      round down floor(x), round up ceiling(x)
    • the sign of a number:
    • for probability theory:
      the error function erf(x) (integral of probability), Laplace function laplace(x)
    • Factorial of x:
      x! or factorial(x)
    • Gamma function gamma(x)
    • Lambert's function LambertW(x)
    • Trigonometric integrals: Si(x), Ci(x), Shi(x), Chi(x)

    The insertion rules

    The following operations can be performed

    - multiplication
    - division
    - squaring
    - cubing
    - raising to the power
    x + 7
    - addition
    x - 6
    - subtraction
    Real numbers
    insert as 7.5, no 7,5


    - number Pi
    - the base of natural logarithm
    - complex number
    - symbol of infinity