幂函数习题精选精讲Selected exercises of power function .doc

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