Several special curves of postgraduate mathematics: Dirichlet function, symbolic function, integer function, hyperbolic sine function and hyperbolic tangent function.

Dirichlet function: It is a periodic function, but there is no minimum positive period. Because all positive rational numbers are their periods.

Symbolic function: y = sgnxx & lt0, y =-1; When x=0, y = 0；; x & gt0，y= 1。

Integer function: y=[x], the graph of this function is trapezoidal, sometimes called ladder curve.

Hyperbolic sine function: y = sh x = (e x-e (-x))/2, which is a monotonically increasing odd function. The curve finally approaches y = 1/2 (e x), corresponding inverse function, inverse hyperbolic sine function, y = arsh x.

Hyperbolic tangent function: its domain is negative infinity, positive infinity, y= th x = sh x/ch x, bounded, with the upper bound of 1 and the lower bound of-1.