1. Variables and constants 1) In a certain change process, quantities with the same value are called constants. In a certain change process, quantities with different values are called variables. 2) In a certain change process, there are two variables: X and Y. When X takes each value, Y takes a unique value. At this point, y is called a function of x, x is also called a "dependent variable" and x is called an "independent variable". (The left side of the equation is a function, and the right side of the equation contains independent variables. ) 3) Functional relationship The formula used to express the functional relationship is called "functional relationship", which is also called the analytical formula of the function. Features: 1. This is an equation. 2. On the left is the function (dependent variable) and on the right is the algebraic expression of the independent variable. 4) The range of the function independent variable is 1. The formula should be meaningful. 2. It is of practical significance to express practical problems. 3. The function value is the function value corresponding to the independent variable. 5) The same function: Two functions whose independent variables and dependent variables have exactly the same value range are called "the same function". 2. Drawing steps of a function image 1): 1. Listing 2. Tracking point 3. Connect line 4. It shows that relation 2) If a point is on the image of a function, then the abscissa and ordinate of this point must satisfy the analytical expression of this function, otherwise it will not. 3. Positive proportional function 1) Generally speaking, it has the form: y=kx(k is constant, k≠0) is called "positive proportional function", where k is called proportional coefficient. 2) Why is k≠0? Because if k=0, y is constant no matter what the value of x is. This function has two variables. So k=0 doesn't hold. 3) Increase or decrease of function When k > 0, the image passes through the first and third quadrants, and with the increase of x, y increases accordingly. When k 0, y increases with the increase of X. When k < 0, y decreases with the increase of X. 4) Linear function and image 1. When k > 0 and b > 0, the function image passes through the first, second and third quadrants. 2. When k > 0 and b = 0, the function image passes through the first and third quadrants and the origin 3. When k > 0 and b < 0, the function image passes through the first, third and fourth quadrants. 4. When k < 0 and b > 0, the function image passes through the first, second and fourth quadrants. 5. When k < 0 and b = 0, the function image passes through the second and fourth quadrants and the origin. 6. When k < 0 and b < 0, the function image passes through the second, third and fourth quadrants. In the image of linear function: k determines the increase or decrease of linear function. (The angle between a straight line and two coordinate axes) B determines the position of the linear function. (the positional relationship between a straight line and the intersection of the Y axis and the X axis) In two linear functions: two (several) function images with the same k but different b are parallel. Two (several) function images with the same b but different k are parallel. K and b are the same, and the images of the two functions overlap. 5) Image drawing 1. Draw at two points: (0, b); (-b/k，0)2。 Translation method: draw y=kx first, and then move b. 6) The values of two functions that are symmetrical about X axis are opposite. The values of two function images k that are symmetrical about the Y axis are opposite to each other.