Example question of a primary function expression, what is a primary function expression

1) When x=0, y= When x=, y=0;

2）k=___b=___

3) When x=5, y= when y=30, x= 2 20 liters of oil is stored in the tank, and the oil flows out of the tank evenly, and the flow rate is 0 2 liters minutes, then the functional relationship between the remaining oil quantity q (liters) in the fuel tank and the outflow time t (minutes) is ( ).

a． b． c． d．

Example 1A spring, with a length of 12cm without hanging objects, will elongate after hanging objects, and the length of the elongation is proportional to the mass of the hanging object. If the total length of the spring is after hanging 3kg of objects, find the total length of the spring as a function of y(cm) and the mass of the hanging object x (kg).

If the maximum total length of the spring is 23cm, find the range of the value of the independent variable x. Analysis: This problem is transformed from a qualitative problem of physics to a quantitative problem of mathematics, and it is also a practical problem, the core of which is that the total length of the spring is the sum of the length of the unloaded and the length of the elongation after load, and the value range of the independent variable can be dealt with by the maximum total length, the maximum elongation, the maximum mass and the actual idea.

Solution: Let the function be y=kx+12

Then, the analytical formula of the function obtained by k= is y=

From 23=: x=22

The value of the independent variable x can be 0 x 22

The general expression for a primary function is: y=kx+b (k is not equal to 0).

A primary function is a type of function, generally in the form of y=kx+b (k, b is a constant, k≠0), where x is the independent variable and y is the dependent variable. In particular, when b = 0, y = kx (k is constant, k ≠ 0), and y is called the direct proportion function of x.

Primary functions and their images are an important part of algebra in junior high school, and they are also the cornerstone of analytic geometry in high school, and they are the key content of the high school entrance examination.

Origin of the function. The term "function" was first adopted by the German mathematician Leibniz in the 17th century, when Leibniz used the word "function" to denote the power of the variable x, i.e., x2, x3, ,....Then Leibniz used the word "function" to refer to all the variables related to the points on the curve, such as the abscissa and ordinate, the length of the tangent, the length of the perpendicular line, and so on.

The expression of the primary function is y=kx+b, the image is a straight line, k is the slope of the straight line, and b is the intercept of the straight line on the y-axis.

The general expression of a primary function expression is.

y kx+b, k is the slope and not 0, b is the intercept, can be any number.

A function of the form y=ax+b(a≠0) is called a primary function. That is, y=ax+b(a≠0).

A one-time functionThe expression is: y=mx+b (m, b is constant, m≠0).

Analysis: where m is the slope and cannot be 0; x represents the independent variable.

b denotes the y-axis intercept.

and m and b are constants. First, the analytic formula of the Zen Wang function is set, and then the unknown slope in the analytic formula is determined according to the conditions, and the analytic formula is obtained from the completion of the analysis. This analytic formula is similar to a straight-line equation.

in the oblique truncated type.

There are three ways to represent a primary function, as follows:1. Analytical method.

The method of expressing a function with an equation containing the independent variable x is called the analytic method.

2. List method.

The method of expressing the relationship between functions in a table corresponding to a series of x values and y columns is called the list method.

3. Image method.

The method of using images to represent the relationship between functions is called the image method.

The general expression for a primary function is: y=kx+b (k is not equal to 0).

A primary function is a type of function, generally in the form of y=kx+b (positive delay, b is constant, k≠0), where x is the independent variable and y is the dependent variable. In particular, when b = 0, y = kx (k is constant, k ≠ 0), and y is called the direct proportion function of x.

Primary functions and their images are an important part of junior high school algebra, and they are also the cornerstone of high school analytic geometry, and they are also the key content of the high school entrance examination.

Origin of the function. The term "function" was first adopted by the German mathematician Leibniz in the 17th century, when Leibniz used the word "function" to denote the power of the variable x, i.e., x2, x3, ,....Then Leibniz used the word "function" to refer to all the variables related to the points on the curve, such as the abscissa and ordinate, the length of the tangent, the length of the perpendicular line, and so on.

Function properties: 1. The change value of y is proportional to the change value of the corresponding x, and the ratio is k.

That is: y=kx+b(k≠0) (k is not equal to 0, and k,b are constants).

2. When x=0, b is the intersection point of the function on the y axis, and the coordinates are (0,b). When y=0, the intersection point of the function image on the x-axis is marked as (-b k,0).

3. k is the slope of the primary function y=kx+b, k=tan (the angle is the angle between the image of the primary function and the positive direction of the x-axis, ≠90°).

4. When b=0 (i.e., y=kx), the image of the primary function becomes a proportional function, and the proportional function is a special one-time function.

5. Function image properties: when k is the same, and b is not equal, the images are parallel; When k is different and b is equal, the images intersect on the y-axis; When k is negative to each other, the two straight lines are perpendicular.

The general expression for a primary function is: y=kx+b (k is not equal to 0).

A function is one of the functions, generally in the form of y=kx+b (k, b is a constant, k≠0), where qihu x is the independent variable and y is the dependent variable. In particular, when b = 0, y = kx (k is constant, k ≠ 0), and y is called the direct proportion function of x. Cavity fluid.

Origin of the function. The term "function" was first coined by the German mathematician Leibniz in the 17th century, when Leibniz used the word "function" to denote the power of the variable x, i.e., x2, x3, ,....Leibniz then used the word "function" to mean the abscissa on a curve.

The ordinate, the length of the tangent, the length of the perpendicular line, and all other variables related to the points on the curve, and in this way the word "function" became popular.

Generally, the undetermined coefficient method is used.

The method of solving the analytic formula of a function by the undetermined coefficient method is called the method of obtaining the desired coefficient method, which first sets the relationship of the function to be solved (which contains unknown constant coefficients), and then lists the equation or system of equations according to the conditions, and finds the coefficient of the variable and the value of constant b, so as to obtain the result. Four steps to solve the problem: Step 1:

Let be the general form of the function. The second step: substitution, substituting the analytic formula to obtain the equation or system of equations.

Step 3: Find the value of the undetermined coefficients k,b by column equation or system of equations. Step 4:

Write, write out the analytic formula of the function.