1, even function:
F(-x)=f(x), that is, the function image is symmetrical about y axis.
2. Odd function:
F(-x)=-f(x), that is, the function image is symmetrical about the origin.
3. Piecewise function
The domain is divided into several segments, and each segment uses a different function expression.
4. Inverse proportional function
F(x)= 1/x, that is, y= 1/x, x is not equal to 0, and its image is hyperbolic.
5. Proportional function
F(x)=kx, that is, y=kx, and k is a constant, which is like a straight line passing through the origin.
6. Power function
F(x)=xn, where n is a constant, an even function when n is a positive even number, and a odd function when n is a positive odd number.
7. Logarithmic function
F(x)=loga(x), where a is constant, a is not equal to 1 and a is greater than 0, and x is greater than 0.
8. Exponential function
F(x)=a~x, where a is a constant and a is greater than 0 and not equal to 1.
9, trigonometric function
Including sine function, cosine function and tangent function, which represent sine value, cosine value and tangent value of an angle respectively, is an important concept in mathematics.
The definition and nature of odd function
I. Definition
1, odd function is defined as, regarding any x of F(x), f (x) = f (-x), that is, the function value of a number and the function value of the reciprocal of this number are reciprocal;
2. odd function corresponds to an even function, contrary to odd function;
3. The graph of odd function is symmetrical about the origin. Function is a very important part of mathematics. By learning functions, we can calculate and solve all kinds of problems, but there are many kinds of functions, and each function has different properties.
Second, nature.
Odd function's graph is centrosymmetric about the origin. Sometimes the title will give a graphic of the function. Let's judge whether this function is odd function or even. If it is centrosymmetric, then this function is odd function, but note that the symmetry point is the origin. If it is an axisymmetric figure, it is an even function, and the axis of symmetry is the Y axis.