How to observe and parse a function, gain insight into its mysteries, and then master a function? How do you look at the one, two, three, and four quadrants of a primary function?
1 Definition of a primary function
A primary function is a function of the form y=kx+b(k≠0), where x and y are variables and k and b are constants. It is a basic and important type of function that is widely used in everyday life and scientific research.
2 Characteristics of primary functions
The main characteristics of the primary function are as follows:
1) Linear properties: The image of a primary function is a straight line.
2) Slope: The slope k of the primary function represents the inclination of the line, which determines the direction of the line in the coordinate system.
3) Intercept: The intercept b of the primary function represents the intersection point of the line and the y-axis, reflecting the position of the line on the y-axis.
4) Monotonicity: When the primary function is k>0, as x increases, y also increases; At k<0, y decreases as x increases.
3 Classification of one, two, three, and four quadrants
According to the division of coordinate axes, the planar Cartesian coordinate system is divided into four quadrants. The first quadrant is located in the positive direction of the x-axis and y-axis, the second quadrant is in the negative direction of the x-axis and the positive direction of the y-axis, the third quadrant is located in the negative direction of the x-axis and the negative direction of the y-axis, and the fourth quadrant is located in the positive direction of the x-axis and the negative direction of the y-axis.
4 Characteristics of one, two, three, four quadrants
1) The first quadrant: x and y are both positive, and the characteristic is that the coordinate values are both positive.
2) The second quadrant: x is negative and y is positive, characterized by negative abscissa and positive ordinate.
3) The third quadrant: x and y are both negative, and the characteristic is that the coordinate values are both negative.
4) The fourth quadrant: x is positive and y is negative, characterized by positive abscissa and negative ordinate.
The performance of a function in each quadrant.
5.1 First Quadrant
In the first quadrant, the image of the primary function tends to rise, and as x increases, so does y. The primary function here can be seen as a special case of the proportional function.
5.2 Second Quadrant
In the second quadrant, the image of the primary function tends to decrease, and as x increases, y decreases. The primary function here can be seen as a special case of the inverse proportional function.
5.3 Third Quadrant
In the third quadrant, the image of the primary function also tends to decline, but unlike the second quadrant, as x decreases, y also decreases.
5.4 Fourth quadrant
In the fourth quadrant, the image of the primary function tends upward, but unlike the first quadrant, y increases as x decreases.
5.5 Observation and Analysis
By observing and analyzing the performance of the primary function in each quadrant, we find that the image of the primary function is not a simple straight line, but contains rich connotations. It not only reflects the motion of the points in the coordinate system, but also reveals the mysteries of the mathematical world.
6 Conclusion
As a basic and important type of function, primary function has a wide range of applications in the field of mathematics. By observing and analyzing the primary function in each quadrant, we can gain insight into its properties and characteristics.