function representation

Definition

Image method

Taking advantage of the monotonicity of known functions

Derivative method

The monotonicity of functions in two different intervals is the same. Generally, they are written separately and do not connect with "," or "and". Do not use ∪

increasing function increasing function = increasing function

Decreasing function Decreasing function = Decreasing function

Same increase and different decrease

functional method

basic inequality method

The domain is not symmetric about the origin

odd function

even function

odd function odd function = odd function

even function even function = even function

Odd function × odd function = even function

Even function × even function = even function

Odd function × even function = odd function

minimum positive period

The constant difference between brackets is periodic

It is a symmetry that the sum inside the brackets is a constant

Double symmetry produces periodicity. The period of the same symmetry (points and points or lines and lines) is 2 times the interval, and the period of different symmetries (points and lines) is 4 times the interval.

Parity

Monotonicity

cyclical

symmetry

translation transformation

Scaling transformation

Symmetric transformation

flip transformation

The existence theorem of zero points can only determine whether there are zero points in the open interval, but cannot determine the number of zero points.