1. Several important concepts of linear functions and proportional functions
1.Definition:
If the relationship between two variables x and y can be expressed as y=kx+b (k and b are constants, and k is not equal to 0)
In the form of , we say that y is a linear function of x. In particular, when b=0, we say that y is a proportional function of x.
Notice:
(1) A proportional function is a linear function, but a linear function is not necessarily a proportional function. That is to say, a proportional function is a special case of a linear function.
(2) Don’t ignore the fact that k in the condition is equal to 0. If k=0, the straight line y=b is not a linear function, which means that the proportional function is a special case of a linear function.
2. Image and properties of linear functions
3. The influence of k and b on the image of a linear function
4. Determination of linear function expression
Use the undetermined coefficient method to list the system of equations according to the conditions to determine the values of k and b, and then find the expression of the linear function. For proportional functions, if the coordinates of a point are known, they can be directly substituted into the analytical formula. For linear functions (b is not equal to 0). It is necessary to know the coordinates of two points and establish a system of equations to obtain the analytical formula.
5. Example explanation
6. Summary:
1. Any number raised to the 0th power that is not equal to 0 is equal to 1.
2. Simple questions on linear functions generally test several points, including the definition of a linear function, the symbol of k, the quadrant it passes through, and the increase and decrease of y with x. The puzzle is usually combined with a quadratic function of one variable, which will be explained in detail later.
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