How to learn functions well, actually. How to learn functions well

For the teacher to understand and memorize what he said in class, it is important to have an appropriate amount of [review] and [do questions] after class, and it is very important to write the logical order in the multi-thinking function, and then it is necessary to have appropriate exercises. Junior high school!? High school.

Don't let go of a summary, although junior high school functions are not much redundant, but high school is all about learning functions, function learning basics, there is no shortcut to learning, only your own efforts, come on...

When learning functions, recognize that functions are an abstract way of thinking mathematically. Don't care too much about whether the topic will be done or not, but start with understanding, to really understand why? Understand that a function is an abstract generalization of a real-world problem.

For example, we use two numbers to represent a point, y=kx+b to represent line segments, and y-ax2+bx+c to represent parabolas. The most important thing is a change in the way of thinking.

Functions in junior high school will be simpler. Mainly primary and quadratic functions.

The content of the primary function is generally relatively simple, and the problem solving skills are mainly to set the analytic formula of the function, and then find the corresponding conditions according to the design.

It is recommended to preview in advance, and then remember that y=kx+b (k is not equal to 0) is in k>0, b>0; k>0,b<0; k<0,b>0;k<0,b<0.

Quadratic functions are a bit more difficult: y=ax 2+bx+c (a is not equal to 0).

It is recommended to start with the image, pay attention to the case of a>0 and a<0, and what is the difference between the axis of symmetry x=-b 2a on the left and right side of the y-axis.

According to the needs of the problem, you can flexibly choose the vertex formula y=a(x-m) 2+n, the two-point formula y=a(x-x1)(x-x2), and the general formula y=ax 2+bx+c solution.

Function function is naturally the most important image, and the big questions in the exam are basically a synthesis of function + geometry.

Therefore, it is necessary to be proficient in function images, function properties, and then brush up on the ......

ps: It is recommended to learn the system of unary quadratic equations + unary quadratic equations first, and observe the relationship between the equation and the image after mastering it, which will have a lot of gains.