(1) This is an even function, just study the x>0 image. When x>0, y =-x? +2x+3=-(x- 1)？ +4? (x>0), as long as you draw the right half of the Y axis, you can draw the whole image. Results: The increasing range of the function is (-∞,-1)∩[0, 1], and the decreasing range of the function is [- 1, 0)∩( 1,+∞). Note: Monotone intervals can be combined.

②

The cardinality is greater than 1, so y = 2 x is the increasing function, that is, the increasing interval of the y function.

y=？ -x？ +x+2 is a parabola with an axis of symmetry x= 1/2 and a downward opening, so it increases when x≤ 1/2 and x >; Decreasing by 1/2

Therefore, the increasing interval of the function F(x) is (-∞, 1/2], and the decreasing interval is (1/2,+∞).

③

From the meaning of the question, we can know that x 2-x-6 ≥ 0, that is, (x-3)(x+2)≥0, and the solution is x≥3. x≤-2

The symmetry axis of function f (x) = x 2-x-6 x= 1/2, the opening is upward, x < = 1/2, the function f (x) decreases, x >；; The function f(x) of 1/2 increases.

Therefore, the increasing interval of y = √ (x 2-x-6) is [3, +∞), and the decreasing interval is (-∞, -2].

④

2-x 2 ≥ 0, that is, -√2≤? x？ ≤√2

The symmetry axis of the image with y = 2-x 2 is x=0, the opening is downward, and x >；; =0 decreasing, x

So f (√ 2-x 2) decreasing interval? [0,√2]