The application of mathematics in life Mathematics is a very useful subject. As early as ancient times, primitive people have been "dabbling in counting" and "knotting notes" Nowadays, mathematical knowledge and ideas are widely used in industrial and agricultural production and people's daily life. For example, after shopping, people should keep an account for year-end statistical inquiry; Go to the bank to handle savings business; Check the water and electricity costs of each household, which makes use of the knowledge of arithmetic and statistics. In addition, the "push-pull automatic telescopic door" at the entrance of the community and government compound; Smooth connection between straight runway and curve in sports field; Calculation of the height of the building whose bottom cannot be closed: determination of the starting point of two-way operation of the tunnel; The design of folding fan and golden section is the property of straight line in plane geometry and the knowledge of solving Rt triangle. So our research topic is the application of mathematics in life. I hope that through this little study, I can improve my mathematics learning ability and consciously use mathematics knowledge in my life. Combine high school knowledge: function, inequality, sequence, etc. We searched the relevant information on the internet and combined with our real life thinking, which is summarized as follows. The first part is the application of functions. The functions we have studied are: linear function, quadratic function, fractional function, irrational function, power function, exponential function, logarithmic function and piecewise function. These functions reflect the dependence of variables in nature from different angles, so the knowledge of functions in algebra is closely related to production practice and life practice. 1. The application of one-dimensional linear function is widely used in our daily life. When people are engaged in business, especially in consumer activities in social life, if the linear correlation of variables is involved, one-dimensional linear function can be used to solve the problem. For example, when we shop, rent a car or stay in a hotel, the operator will provide us with two or more payment schemes or preferential measures for publicity, promotion or other purposes. At this time, we should think twice, dig deep into the mathematical knowledge in our heads and make wise choices. As the saying goes: "From Nanjing to Beijing, it is better to buy than to sell." Never follow blindly, lest you fall into the small trap set by the merchants and suffer immediate losses. Shopping with my family these days, merchants take various preferential measures. I use my own mathematical function to understand and calculate carefully. I went shopping in the "Good Day" supermarket, and an eye-catching brand attracted me. It says that you can get a discount on buying teapots and teacups, which seems to be rare. What's even more strange is that there are actually two preferential ways: (1) sell one get one free (that is, buy a teapot and get one cup) (2) give a 10% discount (that is, pay 90% of the total payment); . There is also a prerequisite: buy more than three teapots (teapot 20 yuan/one, teacup 5 yuan/one). From this, I can't help thinking: Is there a difference between these two preferential measures? Which is cheaper? I naturally thought of the functional relationship, and decided to apply the knowledge of functions I learned to solve this problem by analytical methods. I wrote on the paper: Suppose a customer bought X teacups and paid Y yuan (x>3 and x∈N), then pay Y1= 4× 20+(X-4 )× 5 = 5x+60 by the first method; Use the second method to pay y2=(20×4+5x)×90%=4.5x+72. Then compare the relative sizes of y 1y2. Let d = y1-y2 = 5x+60-(4.5x+72) = 0.5x-12. 0，0.5x- 12 & gt； 0, namely x & gt24; When d=0, x = 24 when d < 0, x