knowledge points of inverse proportional function in senior high school mathematics
A function with the shape of y=k/xk as a constant and k≠ is called an inverse proportional function.
the value range of the independent variable x is all real numbers that are not equal to .
image properties of inverse proportional function: the image of inverse proportional function is hyperbola.
since the inverse proportional function is an odd function with f-x=-fx, the image is symmetrical about the origin.
In addition, from the analytical formula of the inverse proportional function, it can be concluded that any point on the image of the inverse proportional function is perpendicular to the two coordinate axes, and the rectangular area surrounded by this point, the two vertical feet and the origin is constant, which is |k|.
Knowledge points:
1. Any point on the inverse proportional function image is taken as the vertical segment of two coordinate axes, and the area of the rectangle enclosed by these two vertical segments and the coordinate axes is |k|.
2. for hyperbola y=k/x, if any real number is added or subtracted from the denominator, that is, y = k/x mm is a constant, it is equivalent to translating the hyperbola image to the left or right by one unit. Translation to the left when adding a number, and translation to the right when subtracting a number
Knowledge points of logarithmic function in senior high school mathematics
The general form of logarithmic function is that it is actually the inverse function of exponential function. Therefore, the stipulation of a in exponential function is also applicable to logarithmic function.
The graph of logarithmic function is only the symmetric graph of exponential function with respect to the straight line y=x, because they are reciprocal functions.
1 The domain of the logarithmic function is a real number * * * greater than .
2 The range of logarithmic function is all real numbers * * *.
3 functions always pass the point of 1,.
when 4a is greater than 1, it is a monotonically increasing function and convex; When a is less than 1 and greater than , the function is monotonically decreasing and concave.
5 obviously the logarithmic function is unbounded.
knowledge of exponential function in senior high school mathematics
The general form of exponential function is, as we can know from the discussion of power function above, if X can take the whole real number * * * as the domain, then only
can it be obtained that:
1 The domain of exponential function is * * * of all real numbers, and the premise here is that A is greater than , and for the case that A is not greater than .
2 The range of exponential function is a real number * * * greater than .
3 function graphs are concave.
when 4a is greater than 1, the exponential function increases monotonically; If a is less than 1 and greater than , it is monotonically decreasing.
5 we can see an obvious rule, that is, when a tends to infinity from , it can't be equal to , and the curve of the function tends to be close to the position of the monotonically decreasing function of the positive semi-axis of Y axis and the negative semi-axis of X axis respectively. Where the horizontal straight line y=1 is a transition position from decreasing to increasing.
6 functions always tend to the x axis infinitely in a certain direction and never intersect.
the 7 function always passes the point of ,1.
8 obviously the exponential function is unbounded.