It is known that f (x) is an even function on R. if the image of F (x) is shifted one unit to the right, then the image of an odd function is obtained. If f (2) = - 1, then f (1) + F (2) + F (3) + +The value of F (2011) is () A. - 1B. 0C. 1D. Not sure | Math enthusiast | Mathematical art

It is known that f (x) is an even function on R. if the image of F (x) is shifted one unit to the right, then the image of an odd function is obtained. If f (2) = - 1, then f (1) + F (2) + F (3) + +The value of F (2011) is () A. - 1B. 0C. 1D. Not sure

∵ f (x) is an even function on R. the image of ∵ f (x) is symmetric about y axis, that is, the function has symmetry axis X = 0, f (x) = f (- x) & nbsp; X is replaced by X + 1, so f (x + 1) = f (- x-1) and ∵ after the image of F (x) is shifted one unit to the right, an image of odd function is obtained

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1. It is known that f (x) is an even function on R. if the image of F (x) is shifted one unit to the right, then the image of an odd function is obtained. If f (2) = - 1, then f (1) + F (2) + F (3) + +The value of F (2011) is () A. - 1B. 0C. 1D. Not sure
2. How to prove that F1 (x) = f (x) + F (- x) is an even function and F2 (x) = f (x) - f (- x) is an odd function?
3. F1 (x) = f (x) + F (- x) is even function, F2 (x) = f (x) - f (- x) is odd function, right
4. Let a = (cosx, SiNx), B = (cosy, siny), if | √ 2A + B | = √ 3 | - A - √ 2B |, then cos (X-Y)
5. As shown in the figure, in ladder ABCD, ad ‖ BC, ad = 2, BC = 4, point m is the midpoint of AD, and △ MBC is an equilateral triangle (1) Prove: the trapezoid ABCD is isosceles trapezoid; (2) the moving points P and Q move on the line BC and MC respectively, and ∠ MPQ = 60 ° remains unchanged. Let PC = x, MQ = y, find the functional relationship between Y and X; (3) in (2): when the moving points P and Q move to where, the quadrilateral with points P, m and two points in points a, B, C and D as the vertex is a parallelogram? It also points out the number of parallelograms that meet the conditions. ② when y is the minimum, the shape of △ PQC is judged and the reason is given
6. The taxi charging standards in a city are as follows: (1) the starting price is 8 yuan for less than 3 km; (2) for 3 km or more and less than 10 km, an additional 1.7 yuan will be charged for every additional 1 km; for less than 1 km, it will be calculated as 1 km; (3) for 10 km or more, an additional 50% return fee will be charged for every extra kilometer. A person who takes a taxi for 8.2 km will be charged () yuan
7. CD / / EF / / AB, CD = 2, ab = 4. EF bisects the area of trapezoid ABCD and finds the length of EF CD / / EF / / AB, CD = 2, ab = 4. EF bisects the area of the trapezoid ABCD to find the length of EF (requires a problem-solving process)
8. If A-B = B-A and a = 4, B = 3, find the value of a + B
9. As shown in the figure, it is known that in the quadrilateral ABCD, ad ‖ BC, ad > BC, ab = DC, EA = ed, EB and EC intersect ad at points F and g respectively to prove that the quadrilateral fbgc is isosceles trapezoid
10. A mathematics application problem urgent I! Fang Hua's family has a 40 cm long and 25 cm wide glass fish tank with a water depth of 20 cm. One day, Fang Hua accidentally dropped a 10 cm square iron block into the tank. How many cm will the water surface rise? But also the solution ideas and the meaning of each formula! It's up to, remember, it doesn't seem to be up to how many centimeters!
11. It is known that f (x) is an even function on R, f (0) = 2. If the image of F (x) is shifted one unit to the right, then the image of an odd function is obtained. Then the value of F (1) + F (3) + F (5) + F (7) + F (9) is () A. 1B. 0C. -1D. −92
12. It is known that f (x) is an odd function defined on R, and f (1) = 1. If the image of F (x) is shifted one unit to the right, the image of an even function is obtained, Then f (1) + F (2) + F (3) f (4) + F (2011) is equal to
13. As shown in the figure, it is a part of the graph of quadratic function & nbsp; y = AX2 + BX + C (a ≠ 0). The following propositions are given: ① a + B + C = 0; ② b > 2A; ③ two of AX2 + BX + C = 0 are - 3 and 1 respectively; ④ a-2b + C > 0. The correct proposition is () A. ①②B. ②③C. ①③D. ①②③④
14. The graph of quadratic function y = AX2 + BX + C is shown in the figure, then the error in the following relation is A.a＜0 B.c＞0 C.b2-4ac＞0 D.a+b+c＞0 The opening direction is downward, the symmetry axis is x = - 1, and the intersection point with y axis is in the positive half axis
15. Urgently seeking the image of quadratic function y = ax ^ 2 + BX + A ^ 2 + B (a is not equal to 0)
16. Given that the image of quadratic function y = AX2 + BX + 4 intersects with X axis at a and B, two points intersect with y axis at C angle ACB = angle ABC AB = 5, find the analytic expression of the quadratic function
17. The image of quadratic function y = x ＾ 2 - (a + 2) x + 2A (a > 0) intersects with X-axis at two points a and B, intersects with Y-axis at C, and the area of △ ABC is 3~
18. As shown in the figure, let the image of quadratic function y = ax & # 178; + BX + C intersect at two points AB, and intersect with y axis at point C, if AC = 8, BC = 6, ∠ ACB = 90 °
19. If the vertex of the image of quadratic function f (x) = - x ^ 2 + 4x + C is on the X axis, then the value of C is
20. Given that the image of quadratic function y = ax & # 178; + BX + C passes (1,0), and a > b > C, then the value range of C / A is?