Tick-tock function is a general function similar to inverse proportional function, also known as "double hook function", "hook function", "stop function" and "Shuang Yan function". Also known as "Nike function" or "Nike curve".

Hook function (hyperbolic function) is in the form of f (x) = ax+b/x (a > 0). Named after the image.

draw

Image attribute of tick function;

Tick function is a common and special function in mathematics. See the picture. You'd better draw an asymptotic line y=ax when drawing.

Parity monotonicity

When x>0, f(x)=ax+b/x has a minimum value (here, for the convenience of research, a>0, b>0), that is, x=sqrt(b/a) (sqrt stands for finding a quadratic root).

Strange function.

Make k=

, and then:

Interval increase: {x|x≤-k} and {x | x≥k }；;

Negative interval: {x |-k ≤ x

Trend: on the left side of Y axis, increase or decrease, and on the right side of Y axis, decrease or increase are two hooks.

Asymptote

The image of hook function is two hyperbolas with Y axis and y=ax as asymptotes respectively.