Hook function is a general hyperbolic function similar to inverse proportional function, and its form is f (x) = ax+b/x (a >; 0, b>0). Named for its image, it is also called "double hook function", "hook function", "stop function" and "Shuang Yan function". Because the function image is similar to the Nike trademark, it is also called "Nike function" or "Nike curve".

Nike function

draw

Tick function is a common and special function in mathematics. See the picture. You'd better draw an asymptote when drawing.

. In the first interval, the turning point is

Most valuable

When x> is 0,

There is a minimum value (here, a>0, b>0 for the convenience of research). When is this?

F(x) takes the minimum value.

Parity and monotonicity

odevity

The double hook function is an odd number function.

monotonicity

Make k=

, and then:

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

Trend: the left side of Y axis increases first and then decreases, and the right side of Y axis decreases first and then increases, which are two hooks.

Asymptote

The image of hook function is two curves with Y axis and y=ax as asymptotes respectively, any one on the image.

The product of the distance from a point to two asymptotes is exactly the product of the sine value of the included angle of the asymptotes (0- 180) and |b|.