F :x->y(y=f(x),x ∈ x) f: The domain of the rule x:f, Df

F (x) = {| y = f (x), y x ∈ Df} f the range of values for the Rf

Y =f(x),x ∈ x y: Like f(x): Original image

Mapping 3 Elements

  • Domain (x, Df)
  • Range Range (Y)
  • Principle of cause (F)

Y =f(x) y: dependent variable x: independent variable f: correspondence relation, that is, function definition domain: value range of independent variable

The graph of an odd function is symmetric about the origin, and the graph of an even function is symmetric about the Y-axis

Periodic function: If there exists a positive number T such that f(x)=f(x+T), which is true for any real number x, then y=f(x) is a periodic function

  • The sine function y=sinx and the cosine function y=cosx have a period of 2π
  • The tangent function y equals tangent x and the cotangent function y equals cotangx have period π

The necessary and sufficient condition for the function y=f(x) to have an inverse function is that for any x1,x2, if x1 is not equal to x2, then f(x1) is not equal to f(x2), in particular, monotone functions have an inverse function

The unit circle centered at the origin of the coordinates can be expressed by the equation x^2+y^2=1. If we only consider the upper semicircle, we can get y=√1-x^2 from the equation x^2+y^2=1; If we only consider the semicircle, we can get y=-√1-x^2 from the equation x^2+y^2=1; Therefore, y= square root of 1-x^2 and y= -square root of 1-x^2 are both determined by x^2+y^2=1, and are called implicit functions.

If the function y = f (x) satisfy the equation f = (x, y) = 0, namely f (x, f (x) = 0, the yue: y is a equation f = (x, y) = 0 x as determined in implicit function