How to find the symmetry axis, monotonicity and parity of trigonometric functions?
Based on the most primitive trigonometric function, you can understand the meaning of a, W, and φ respectively. Then you can understand these properties of this simple function, which is half successful, and then you can infer by analogy
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- 1. Let y = f (x) be an odd function on the domain R, and f (X-2) = - f (x) holds for all x belonging to R, then the symmetry axis of F (x) image?
- 2. If the function defined on R, y = f (x), and the image of y = f (x + 2) is symmetric with respect to x = 0, then the symmetry axis of the image of the function y = f (x)
- 3. Given the function f (x) = log, take a as the base 1 + X / 1-x (a > 0, a ≠ 1) to find the inverse function
- 4. The inverse function of function f (x) log with base 2 (x + 1) (x > = 0) is f ^ - 1 (x)=
- 5. If the inverse function of function f (x) is f ^ (- 1) (x) = log with 2 as the base x, then f (x)=
- 6. The inverse function f ^ - 1 (x) = () of function f (x) = log (2) (1 + 1 / x) (x > 0)
- 7. The monotone increasing interval of function f (x) = log5 (2x + 1) is______ .
- 8. The monotone increasing interval of function f (x) = log5 (2x + 1) is______ .
- 9. Given that the function f (x) = log (2∧x-1) (a > 0, and a ≠ 1) always has f (x) > 0 in the interval (0,1), then the monotone increasing interval of the function y = log ∨ a (X & # 178; - 2x-3) is
- 10. The monotone increasing interval of the function y = log12 (x2 − x − 6) is______ .
- 11. What is the relationship between derivative function and monotonicity of function? What is the relationship between derivative function and monotonicity of function? How to draw function image by derivative function, or draw derivative function by function? Please give specific examples. Is there a better way to remember them?
- 12. Draw the graph of function f (x) = | x ^ 2 + X-2 | and write the monotone interval
- 13. Let the function FX = x + A / x + B (a > b > 0), find the monotone interval of F (x), and prove the increasing of F (x) in its monotone interval Sex
- 14. F (x) = x2 + 4x + 3, t ∈ R, the function g (T) represents the minimum value of function f (x) in the interval [T, t + 1], and the expression of G (T) is obtained
- 15. The minimum value of the function f (x) = x2-4x-4 in the closed interval [T, t + 1] (t ∈ R) is denoted as G (T). (1) try to write the functional expression of G (T). (2) make the image of G (T) and find the minimum value of G (T)
- 16. Let f (x) = x2-2x + 2, the minimum value of X ∈ [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
- 17. Let f (x) = x2-2x + 2, the minimum value of X ∈ [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
- 18. FX = x ^ 2-2x + 2, X ∈ [T, t + 1], t ∈ R, find the expression of the minimum value g (T) of function FX
- 19. Let f (x) = x ^ 2-2x + 2, let the minimum value of F (x) on [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
- 20. Let f (x) = x2-2x + 2, the minimum value of X ∈ [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)