1, define a function with the shape of y=xα as a power function, where α is a constant, and middle school only studies the case that α is a rational number.

Second, exponential function and logarithmic function:

1, definition: exponential function, y = ax (a > 0, and a≠ 1), pay attention to the difference with power function. The logarithmic function y = logax (a > 0 and a≠ 1). Exponential function y=ax and logarithmic function y=logax are reciprocal functions.

2. the image and properties of exponential function: y = ax (a > 0 and a≠ 1) and logarithmic function y = logax (a > 0 and a≠ 1).

Third, exponential equation and logarithmic equation:

Exponential equation and logarithmic equation belong to transcendental equation. In middle school, just solve some simple and special types of exponential equations and logarithmic equations. The basic idea is to turn them into algebraic equations to solve.

Fourth, the concept of order:

1, sequence definition: a series of numbers arranged in a certain order is called a sequence; ? Each number in a series is called an item in this series. Let's write it as na, and the item at the first position of the series is called 1 item (or the first item). The item in the second position is called Item 2, ... and the serial number is n? The item of is called the nth item (also called the general item) and is recorded as na.

Verb (abbreviation of verb) function representation:

There are three commonly used methods to express functions: analytical method, list method and image method.

Analytical method: it is to express the corresponding relationship between two variables with mathematical expressions.

List method: it is to list tables to represent the corresponding relationship between two variables.

Mirror image method: that is, images are used to represent the corresponding relationship between two variables.

Six, the function of image:

1, which determines the domain of the function;

2. Analytic resolution function;

3. Discuss the properties of functions (parity and monotonicity);

4. Draw the image of the function.

Seven, the use of basic function image transformation diagram:

It is necessary to accurately remember the images of various basic elementary functions such as linear function, quadratic function, inverse proportional function, exponential function, logarithmic function, power function and trigonometric function.