幂函数习题精选精讲1（Selected exercises of power function 1）power function
As the main function of high school mathematics, throughout the high school mathematics learning always, and the power function is a part of which, though it simple, but contains some important mathematical ideas. The analysis of several cases, in order to expand students' thinking.
First, the idea of classified discussion
Example 1, the image of the known function and the two axis have no common point, and its image about the Y axis symmetry, the value of N, and draw the function of the image
Solution: since there is no common point between the image and the Y axis, the image is symmetrical about the Y axis, even if it is even
At that time, not even;
At that time, even numbered;
At that time, even numbered;
At that time, not even;
At that time, even numbered;
So n is, 1 or 3.
At this point, the power function is interpreted as or, and its image is shown in Figure 1
Two, the idea of combining numbers and shapes
Example 2 the known point is on the image of the power function, points on the image of the power function
When asked why x is worth: (1); (2); (3)
Analysis: by the definition of power function, first find and parse the formula, and then use the image to judge
Solution: set by you to,
So, that is. Then by order, you have to,
So, that is made. In the same coordinate system
And the image, as shown in Figure 2, is illustrated by the image:
(1) when or when,;
(2) at that time,;
(3) when and when
Summary: the combination of numbers and shapes has important applications in the discussion of inequality, and pays attention to the implicit conditions in this topic
Three, the mathematical idea of transformation
Example 3 the domain of the function is all real numbers, and the range of the real number m is ()
A.
B.
C.
D.
Resolution: if the domain of the function is all real numbers, it can be converted to all real numbers, that is, and
B
Three kinds of discussion questions in power function
The so-called classification discussion, the essence is "to crush one by one, break up the whole into parts, zero for the whole plot strategy. Classification discussion should focus on understanding and mastering the principles, methods and skills to determine the object classification, all clear classification standards, classification discussion is not heavy, no leakage. In power function, classification discussion the idea of an important embodiment, according to the image and the nature of power function, on the basis of monotonity power function are discussed, the results can be achieved.
