Exponential function and logarithmic function are two important basic functions in senior high school. Like other functions, it is still required to master the definition, three elements, images and properties of functions.

The exponential function is y= constant to the power of x, where x is in the exponential position, the base is greater than 0, and it is not 1. Its image means loyalty, passing through a fixed point (0, 1), with a cardinal number greater than 1 as a stroke, and a cardinal number greater than 0 and less than 1 as a stroke. When the base is a pair of reciprocal numbers, the image is symmetric about y axis.

The logarithmic function is the logarithm of y= x based on 0 instead of 1, and the real number x is greater than 0. Its image means lying and being loyal, which is beyond the fixed point (1, 0). When the basis is a pair of reciprocal, the image is symmetrical about X.

Whether exponential function or logarithmic function, the base greater than 1 is a increasing function, and the base greater than 0 and less than 1 is a decreasing function.

Exponential function and logarithmic function

2. Basic problems

Find areas of definition and value. There are three points to pay attention to in finding the domain: the formula under even root number is greater than or equal to 0, the denominator is not 0, and the real number is greater than 0.

Over-fixed point problem.

Ratio size: 1) Using monotonicity ratio; 2) The ratio of media used is 0 and 1.

Compound function question type: 1) decomposition; 2) Study one by one; 3) Solve problems comprehensively.