1, linear function
Linear function is a kind of function, and its general form is y=kx+b(k, b is constant, k≠0), where x is independent variable and y is dependent variable. Especially when b=0, y=kx(k is constant, k≠0), and y is called the proportional function of x.
Linear function and its image are the important contents of algebra in junior high school, the cornerstone of analytic geometry in senior high school, and the key contents of senior high school entrance examination.
2. Quadratic function
The basic expression of quadratic function is y=ax? +bx+c(a≠0). The highest degree of a quadratic function must be quadratic, and the image of a quadratic function is a parabola whose symmetry axis is parallel or coincident with the Y axis.
If the value of y is equal to zero, a quadratic equation can be obtained. The solution of this equation is called the root of the equation or the zero of the function.
3. Positive proportional function
Generally speaking, the relationship between two variables x and y can be expressed as a function with the shape of y=kx (k is a constant, the degree of x is 1, k≠0), so y=kx is called a proportional function.
Proportional function belongs to linear function, but linear function is not necessarily proportional function, it is a special form of linear function.
4. Inverse proportional function
Generally speaking, if the relationship between two variables X and Y can be expressed by Y = K/X (where K is a constant and k≠0), then Y is said to be an inverse proportional function of X. ..
The inverse proportional function image belongs to two centrally symmetric curves with the origin as the symmetry center, and each curve in each quadrant in the inverse proportional function image will be infinitely close to the X axis and the Y axis but will not intersect with the coordinate axis (y≠0).
5, trigonometric function
Trigonometric function is one of the basic elementary functions, which takes the angle (the most commonly used radian system in mathematics, the same below) as the independent variable, and the angle corresponds to the coordinates where the terminal edge of any angle intersects with the unit circle or its ratio as the dependent variable.
Common trigonometric functions are sine function, cosine function and tangent function.
6. Exponential function
Exponential function is one of the important basic elementary functions. Generally y=ax (a is a constant, take a >；; 0, a≠ 1) is called exponential function, and the domain of the function is R.
Note that in the definition expression of exponential function, the coefficient before ax must be the number 1, and the independent variable x must be in the position of exponent, and it cannot be any other expression of x, otherwise it is not an exponential function.
7. Logarithmic function
In general, the function y = logax(a >；; 0, and a≠ 1) is called logarithmic function, that is, a function with power (real number) as independent variable, exponent as dependent variable and base constant as constant is called logarithmic function.
Where x is the independent variable and the domain of the function is (0, +∞), that is, x >；; 0。 It is actually the inverse function of exponential function, which can be expressed as x=ay. Therefore, the stipulation of a in exponential function is also applicable to logarithmic function.