Draw the function y = | x-3 | + X + 1 |, and find out the value range of the function, important figure

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• 1. Given the function f (x) = x + 1 + X-2, draw the image of the function I'm in a hurry!
• 2. It is known that the quadratic function FX = AX2 + BX (a, B are constants, and a is not equal to 0) satisfies the following conditions: F (- x + 5) = f (x-3), and the equation f (x) = x has real roots (1) Find the analytic expression of F (x); (2) whether there are real numbers m, n (m < n), so that the definition field and value field of F (x) are [M, n] and [3M, 3N]? Request the value of M, n
• 3. It is known that the vertex coordinates of the quadratic function y = f (x) are (3 / 2,49), and the difference between the two real roots of the equation f (x) = 0 is equal to 7,
• 4. When the vertex of the image of quadratic function f (x) is known, m (- 2 / 3,49), the difference between the two equations f (x) = 0 is equal to 7, and the analytic expression of quadratic function f (x) is obtained
• 5. It is known that the vertex coordinates of the quadratic function y = f (x) are (- 32,49), and the difference between the two real roots of the equation f (x) = 0 is equal to 7
• 6. Given the function f (x) = - A & # 178; X & # 179 / / 3 + ax & # 178 / / 2 + CX (a is not equal to 0), when a ≥ 1 / 2, if the real number equation f '(x) = 0 When a ≥ 1 / 2, if the real number equation f '(x) = 0 has two real number roots m, N, and | m | ≤ 1, | n | ≤ 1. Prove: - 1 / 4 ≤ C ≤ A & # - A
• 7. Given quadratic function, f (x) = ax & # 178; + BX + C (a ≠ 0), this paper proves that the equation f (x) = 1 / 2 [f (0) + F (1)] has two unequal real roots, and one root is in the interval (0,1)
• 8. The quadratic function y = f (x) satisfies f (3 + x) = (3-x), and f (x) = 0 has two real roots x1, x2?
• 9. If the quadratic function y = f (x) satisfies f (3 + x) = f (3-x), and f (x) = 0 has two real roots X1 and X2, then X1 + x2 = () A. 0b. 3C. 6D. Not sure
• 10. Function y = ax & # 178; + BX + C (a ≠ 0) image vertex is (1,4) and C = 0, the triangle area formed by the intersection of the vertex of quadratic function and coordinate axis is__
• 11. Draw the graph of the function f (x) = Log1 / 3x-1, and answer with the graph: when is the real number k, the equation Log1 / 3x-1 = k has no solution? The equation is logarithm-1 of absolute value Log1 / 3 bottom X
• 12. The function f (x) = | X-1 | - | x + 2 | (1) the function is expressed in the form of piecewise function; (2) the image of the function is drawn in the coordinate given on the right; (3) the definition domain, value domain, parity and monotone interval of the function are written out (no proof is required)
• 13. The graph of function y = | 3 ^ X-1 | is given, and the value of K is pointed out. When the equation | 3 ^ X-1 | = k has no solution, how many solutions The graph of function y = | 3 ^ X-1 | is given, and the value of K is pointed out. When the equation | 3 ^ X-1 | = k has no solution, it has two solutions Why there are two intersections when 0 < K < 1
• 14. Judge the parity of F (x) = 1 + SiNx − cos2x1 + SiNx
• 15. Judge the parity of the following functions: F (x) = x power of a minus 1 / 2 (a is greater than 0 and a is not equal to 1)
• 16. Judge the parity of F (x) = 1 / A to the power of X + 1-1 / 2 (a is greater than 0 and a is not equal to 1)
• 17. Given the function f (x) = (12x-1 + 12) SiNx & nbsp; (- π 2 < x < π 2 and X ≠ 0) (1) judge the parity of F (x); (2) prove that f (x) > 0
• 18. It is known that the intersection of the line y = 2x-1 and the two axes is a and B respectively, and the image with function y = 2x square passes through a and B after translation RT 1. Find the analytical formula of parabola after translation 2. Calculate the vertex coordinates of the function image after translation [this question is the 14 questions on P31 of ninth grade mathematics class training (Zhejiang Education Edition)]
• 19. It is known that the image of parabola y = the square of minus two-thirds x + four-thirds x + 2 intersects with X-axis at two points a and B, intersects with Y-axis at point C, the symmetry axis of parabola intersects with X-axis at point D, and point m starts from point O and moves to point B at a speed of 1 unit length per second. Point m is perpendicular to x-axis and intersects object line at point P (1) Find the coordinates of point B and point C; (2) Suppose that the area of the quadrilateral OmpC is s when the point m moves x (seconds), find the functional relationship between S and X, and point out the value range of the independent variable x
• 20. Y = x square - 2 | x + 1 | - 1 how to draw an image