The side length of a square is 4. If the side length decreases x, the area decreases y. write out the functional expressions of Y and X. find the value range of the independent variable x

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• 1. The side length of the square is x, and the perimeter is y. please write the functional relationship between Y and X, and write the value range of the independent variable (1) How to draw the graph of this function? (2) What are the basic steps of drawing function images?
• 2. There is a relation between square area s and side length a, where () is an independent variable and () is a function of ()
• 3. For example, for the function y = X-1, let y = 0, we can get x = 1, we say that 1 is the zero of the function y = X-1. It is known that the function y = x2-2mx-2 (M + 3) (M is a constant). (1) when m = 0, find the zero of the function; (2) prove that no matter what value m takes, the function always has two zeros; (3) let the two zeros of the function be respectively The intersection of function image and X axis is a and B respectively (point a is on the left side of point B), and point m is on the line y = X-10. When Ma + MB is the minimum, the function analytic expression of line am is obtained
• 4. For example, for the function y = X-1, let y = 0, we can get x = 1, we say 1 is the function y = X-1
• 5. For example, for the function y = X-1, let y = 0, we can get x = 1, we say 1 is the zero point of the function y = X-1 The known function y = x 2 - 2mx - 2 (M + 3) (M is a constant) (1) When m = 0, find the zero point of the function; (2) It is proved that no matter what value m takes, the function always has two zeros; (3) Let the two zeros of the function be x 1 and x 2 respectively. At this time, the intersection of the function image and the X axis is a and B respectively (point a is on the left side of point B), and point m is on the line y = X-10. When Ma + MB is the minimum, the analytic expression of the function of the line am is obtained
• 6. What function formula does excel use to count the number of values in the table? If there are several numbers in the table (- 1, - 2, - 3, - 4, - 5, - 6,0,1,2,3,4,5,6), use the formula to find out ≤ - 3, - 3 〈? Number ≥ 0, number > 0
• 7. When I assign homework to students, I design three tables: the answers are encrypted and hidden. When students do homework, they can check whether they fill in correctly in the marking form. Only if the values are the same, they can put G1, "correct" and "wrong" in the marking form, But the students filled in the result of the oral calculation. Obviously, it can't be judged as correct. How can we judge that the two tables are not only of the same value, but also of the same formula or function? Supplement: since it is a form of marking, there are more than three or two judgments, such as the score sheet, total score, ranking, passing rate, highest score and so on
• 8. When the value of independent variable x satisfies what conditions, the value of function y = three-thirds of X + 6 satisfies the following conditions? （1）y=0 （2）y＜0 （3）y＞0 （4）y＜2
• 9. What kind of function is y equal to 1 when the independent variable x is 0, and y equal to 0 when the independent variable x is finite It should be found in hyperbolic function or other trigonometric function
• 10. For the function y equals x + 1 / X_ 1, when the value of the independent variable x is? The function value is equal to 0
• 11. Is the necessary and sufficient condition for a function to be a when x tends to infinity?
• 12. On the limit of function: the numerator is LNX, and the denominator is x ^ a (a > 0). The limit of this number can be obtained by variable substitution, and X tends to infinity
• 13. If the limit of function 1 / (x ^ 2) is positive infinity at x = 0, is there a limit at x = 0?
• 14. If the absolute value of P is less than 1, then the power of limp is n, where n is infinite and infinitesimal. Then why is this limit equal to 0
• 15. Limit problem the problem of infinity and infinitesimal Please give examples to illustrate that the following three propositions are wrong 1. The product of infinitesimals is infinitesimal 2. Infinity plus infinity is infinity 3. Infinity multiplied by bounded quantity is infinity
• 16. Does limit infinity and infinitesimal exist
• 17. Is limit equal to infinity the existence or non existence of limit?
• 18. The reciprocal of infinitesimal is infinity. How to understand it? For example, LIM (x ^ 2 + 2x-3) / (4x-1) = 0, why is its reciprocal infinite? This function is not always nonzero n-1
• 19. The reciprocal of infinity is infinitesimal, and the reciprocal of constant not zero is infinity period Can you make it clear why it is a variable
• 20. As far as I know, we use the ratio limit of two infinitesimals to reflect the speed of two infinitesimals approaching zero. When their ratio limit is equal to - 1, is it equivalent? For example, when x → 0, X and - X are infinitesimals, and the limit of their ratio is equal to - 1, so they tend to zero at the same speed. Theoretically, they are equivalent, but the equivalent definition of Infinitesimal in advanced mathematics textbooks is that the ratio limit is equal to 1, not the absolute value of the ratio limit is equal to 1