The Nike function is a general hyperbolic function similar to the inverse proportional function. It is a function of the form f(x)=ax b/x (agt; 0, bgt; 0) . Named after the image, it is also known as the "double hook function", "hook function", "check mark function", "double flying swallow function", etc. Because the function image is similar to the Nike trademark, it is also known as the "Nike function" or "Nike curve".

Properties

Image

The image of the tick function is two curves with the y-axis and y=ax as asymptotes respectively, and any The product of the distances from a point to two asymptotes is exactly the product of the sine of the angle between the asymptotes and |b|.

If agt; 0, bgt; 0, in the first quadrant, The turning point is ?.

Maximum value

When the domain is ?, ? (agt; 0, bgt; 0) takes the minimum value at ?, and the minimum value is ?.

When the domain is ?, the function has no maximum value.

When the domain is ?, ? (agt; 0, bgt; 0) takes the maximum value at ? , the maximum value is?.

Odd-even Monotonicity

Parity

The tick function is an odd function.

Monotonicity

Let k=?, then:

Increasing interval: {x|x≤-k} and {x|x≥k}; decreasing interval: {x|-k≤xlt;0} and {x| 0lt;