The tick function is a general hyperbolic function similar to the inverse proportional function. It is a function of the form f(x)=ax+b/x (a>0,b>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 resembles the Nike trademark, it is also known as the "Nike function" or "Nike curve".
Tick function
Image
The check function is a common and special function in mathematics, as shown in the picture, it is best when drawing Draw the asymptote
. In the first interval, the turning point is
maximum value
When x>0,
has a minimum value (here for the convenience of research, a> 0, b>0), that is, when
, f(x) takes the minimum value.
Odd-even, monotonicity
Parity
The double hook function is an odd function.
Monotonicity
Let k=
, then:
Increasing interval: {x|x≤-k} and {x |x≥k}; decrease interval: {x|-k≤x<0} and {x|0 Change trend: first increase and then decrease on the left side of the y-axis, on the y The right side of the axis first decreases and then increases, which is two ticks. Asymptotes The image of the tick function is two curves with the y-axis and y=ax as asymptotes respectively, and any one on the image