Constant: A quantity that has a fixed value during a certain change process

Variable: A quantity whose value will change during a certain change process

Judgment criteria: See whether the value of the quantity changes during the change process

y=4x2

Definition: Generally, if the variable y changes with the variable x, and for each value of x, y has a unique value corresponding to it, then y is said to be a function of x, recorded as y=f(x), At this time, x is called the independent variable and y is called the dependent variable.

Integer type (y=4x 1)——all real numbers

Fractional type (y=A/B)——x≠0

Radical type (y=√A)——A≠0

Zero power type (y=Aº)——a≠0

Analytical method is convenient List method clear Image method intuitive

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Proportional function A function of the form y=kx (k is a constant, k is not equal to zero) is called a proportional function

A function of the form y=kx b(k, b is a constant, k is not equal to zero) is called a linear function.

k1k2=-1

linear equation of one variable → linear function ax b=0→y=ax b

Angle of number: When y=0, the value of x

Image angle: the abscissa of the intersection of straight line y=ax b and the axis

Solution of the equation

linear inequality of one variable → linear function ax b>0→Above the X-axis ax b<0→below the X-axis

Determine the value range of y through the abscissa coordinate of the intersection of the image and the x-axis

The intersection point of the two lines is the solution set

Solve the analytical expressions of different segments using the method of undetermined coefficients

The x values ​​of different segments have different value ranges

Use the properties of the k value to determine the final value

Shape: The graph of the proportional function y=kx is a straight line passing through the origin

Two-point method: Generally choose (0, 0) (1, k) two points to draw the picture

When k>0, the straight line y=kx passes through one or three quadrants, and y increases with the increase of x.

When k<0, the straight line y=kx passes through the second and fourth quadrants, and y decreases as x increases.

The larger (smaller) the value of |k|, the steeper (slower) the image is.

Shape: a straight line

Two-point method: General selection (-b/k, 0) (0, b)

When k>0, b>0, the straight line y=kx b passes through the first, second, and third quadrants, and y increases with the increase of x.

When k>0, b<0, the straight line y=kx b passes through the first, third, and fourth quadrants, and y increases with the increase of x.

When k<0, b>0, the straight line y=kx b passes through the first, second, and fourth quadrants, and y decreases as x increases.

When k<0, b<0, the straight line y=kx b passes through the second, third, and fourth quadrants, and y decreases as x increases.

"Suppose" establish the general formula of a linear function "Substitute" into a set of corresponding values "Solution" solve this system of equations to find the values ​​of k and b "Substitute" k and b to get the analytical formula of the linear function