Chapter 17 points for reviewing scores

1, the formula with the shape of AB(A and B are algebraic expressions, B contains letters, and B≠0) is called a fraction. Algebraic expressions and fractions are collectively called rational forms.

2. When the denominator is ≠0, the score is meaningful. When the denominator = 0, the score is meaningless.

3. When the score is 0, two conditions must be met at the same time: numerator = 0 and denominator ≠0.

4. Basic properties of the fraction: both the numerator and denominator of the fraction are multiplied or divided by the same algebraic expression that is not 0, and the value of the fraction remains unchanged.

5. The signs of the fraction, numerator and denominator can be changed at will, and the value of the fraction remains unchanged.

6. Four Fractional Operations

1) The key to the addition and subtraction of fractions is general division. Fractions with different denominators are transformed into fractions with the same mother, and then operations are performed.

2) When multiplying and dividing fractions, factorize the numerator and denominator first, and then omit the same factor.

3) the mixed operation of fractions, pay attention to the change of operation order and sign,

4) The final result of fractional operation should be reduced to the simplest fractional or algebraic expression.

7. Fractional equation

1) fractional simplification cannot be confused with solving fractional equations. Fractional simplification is an identical deformation, and the denominator cannot be removed at will.

2) Steps of solving the fractional equation: firstly, the fractional equation is transformed into an integral equation; Second, solve the whole equation; Third, check the roots and remove the added roots through inspection.

3) The steps of solving related application problems are the same as those of listing integral equations to solve application problems: setting, listing, solving, testing and answering.

Chapter 18 review points of functions and images

1, and the straight line specifying the origin, positive direction and unit length is called the number axis. Points on the number axis correspond to real numbers one by one. If the coordinates of point A and point B on the number axis are x 1 and x2, then AB =.

2. Two number axes have a common origin and are perpendicular to each other, forming a plane rectangular coordinate system. Points on the coordinate plane correspond to ordered real number pairs one by one.

3. The points on the coordinate axis do not belong to any quadrant. The ordinate of this point on the x axis y = 0；; The abscissa of a point on the y axis x = 0.

Point x > in the first quadrant; 0，y & gt0; Point x in the second quadrant

Therefore, for the point above the X axis, the ordinate y > 0；; The point below the X axis, the ordinate y < 0；; The point on the left side of the Y axis, the abscissa x < 0；; The point on the right side of the y axis, the abscissa x > 0.

4. For a point symmetrical about a coordinate, the coordinate of this axis is unchanged, and the coordinate of the other axis is opposite. For a point with symmetrical origin, the vertical axis and the horizontal axis are opposite. About the point where the bisector of the first quadrant and the third quadrant are symmetrical, the abscissa and ordinate are interchanged; With regard to the symmetrical points on the bisector of the second quadrant and the fourth quadrant, not only the abscissa and the ordinate exchange positions, but also they become opposite numbers.

5. The horizontal and vertical coordinates of the points on the bisector of the first quadrant and the third quadrant are equal; The horizontal and vertical coordinates of the points on the bisector of the second and fourth quadrants are opposite to each other.

6. In a changing process, there are two variables X and Y. For each value of X, Y has a unique value corresponding to it, so we say that Y is a function of X. X is an independent variable and Y is a dependent variable. The expression methods of functions are: analytical method, image method and list method.

7. The range of independent variables of the function: ① When the analytic expression of the function is algebraic expression, all independent variables can be real numbers; (2) When the analytic expression of the function is a fraction, the value of the independent variable should make the denominator ≠ 0; ③ When the analytic formula of the function is a quadratic root, the value of the independent variable should make the root sign ≥ 0. (4) When the analytic expressions of the function are negative integer exponent and zero exponent, the cardinality is ≥ 0; ⑤ To embody the functional relationship of practical problems and make practical problems meaningful.

8. if y = kx+b (k and b are constants, k≠0), then y is called a linear function of x, if y = kx (k is a constant, k 0), then y is a proportional function of X.

9. The algebraic meaning of a point on a function image is that the coordinates of the point satisfy the analytical formula of the function. The algebraic significance of the intersection of two functions is that the solution of the equations formed by the analytical expressions of the two functions is the intersection coordinates.

10 and the properties of linear function y = kx+b;

The image of (1) linear function is a straight line passing through two points. The larger the value of |k|, the closer the image is to the y axis.

(2) when k >; 0, the image passes through one or three quadrants, and y increases with the increase of x; From left to right, the image is rising (lower left and higher right);

(3) When k < 0, the image passes through two or four quadrants, and y decreases with the increase of x, and from left to right, the image decreases (the left is higher and the right is lower);

(4) When b>0, the intersection point (0, b) with the Y axis is on the positive semi-axis; When b<0, the intersection (0, b) with the Y axis is on the negative semi-axis. When b = 0, the linear function is a proportional function and the image is a straight line passing through the origin.

(5) When several straight lines are parallel to each other, the values of k are equal and b are not equal.

1 1, if y = kx (k is constant, k≠0), then y is called the inverse proportional function of x.

12, the property of inverse proportional function y = kx;

(1) The image of the inverse proportional function is a hyperbola, which is infinitely close to the X and Y axes.

(2) when k >; 0, the two branches of the image are located in the first and third quadrants. In each quadrant, y decreases with the increase of x, and the image decreases from left to right (lower left and upper right).

I'm glad to answer the landlord's question. Please forgive me if there is any mistake.