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"Graphic of a linear function" linear function PPT courseware 4
1. Definition of function graph:
Take the values of the independent variable x and the corresponding dependent variable y of a function as the abscissa and ordinate respectively, and draw its corresponding points in the rectangular coordinate system. The resulting graph composed of these points is called the image of the function.
2. General steps for making function graphs:
(1) List: Select the representative independent variable values and the corresponding values of the function to form a table;
(2) Draw points: Use the value of the independent variable as the abscissa, the corresponding function value as the ordinate, and draw each point in the table in the coordinate system;
(3) Connection: Connect all points with a smooth curve in the order of independent variables from small to large.
New knowledge exploration
(1) In the following two functions, as the value of x increases, how do the values of y change?
As the value of x increases, the value of y increases respectively
(2) Which straight line forms the largest acute angle with the positive direction of the x-axis? Which straight line makes the smallest acute angle with the positive x-axis?
The larger the |k|, the faster the y value increases.
(3) Where is the straight line?
k>0, the straight line passes through the first and third quadrants
Properties of the proportional example function y=kx:
(1) When k>0, the straight line passes through the first and third quadrants, and the value of y increases as the value of x increases;
(2) When k<0, the straight line passes through the second and fourth quadrants, and the value of y decreases as the value of x increases.
Properties of the linear function y=kx+b:
(1)k>0, the value of y increases as the value of x increases
① When b>0, the straight line passes through the first, third, and second quadrants;
②When b<0, the straight line passes through the first, third and fourth quadrants.
(2) When k<0, the value of y decreases as the value of x increases.
① When b>0, the straight line passes through the second, fourth, and first quadrants;
②When b<0, the straight line passes through the second, fourth and third quadrants.
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