Mapping f: a —— > B and f is the corresponding rule among the three elements of a function, and it is actually an algorithm. For example, F(x)=2x+ 1, and f means twice x plus 1.

The modern definition of a function is to give a set of numbers A, assume that the element in it is X, apply the corresponding rule F to the element X in A, and record it as f(x) to get another set of numbers B, assume that the element in B is Y, and the equivalent relationship between Y and X can be expressed as y=f(x).

The concept of function consists of three elements: domain A, range B and corresponding rule F, among which the core is corresponding rule F, which is the essential feature of function relationship.

Function properties:

A quadratic function is a parabola, but a parabola is not necessarily a quadratic function. The parabola of the opening up or down is a quadratic function. Parabola is an axisymmetric figure.

The symmetry axis is a straight line x = -b/2a, and the only intersection point between the symmetry axis and the parabola is the vertex p of the parabola. Especially when b=0, the symmetry axis of the parabola is the Y axis (that is, the straight line x=0).