"Looking at equations (groups) or inequalities from the perspective of functions" linear function PPT courseware 3

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"Looking at equations (groups) or inequalities from the perspective of functions" linear function PPT courseware 3

1. Scenario introduction

1. Solve the inequality 5x+6>3x+10

Solution: The inequality 5x+6>3x+10 can be transformed into 2x-4>0. Solve this inequality to get x>2

Thinking: Can all inequalities be transformed into the form ax+b>0?

2. When the independent variable x has what value, the value of function y=2x-4 is greater than 0?

Solution: The solution to this problem is to solve the inequality 2x-4>0, and it is concluded that when x>2, the value of the function y=2x-4 is greater than 0

Think: Are these two questions the same question?

2. Explore new knowledge

Question 2. When the independent variable x has what value, the value of function y=2x-4 is greater than 0?

Thinking: Can question 2 be explained with a function graph?

1. Let’s first observe the graph of function y=2x-4 to see if we can solve problem 2.

It can be seen that when x>2, all points on the straight line y=2x-4 are above the x-axis, that is, y=2x-4>0. It can be seen that the solution to the inequality can also be obtained through the function graph as x>2

Thinking: Based on the above two questions, can you tell the relationship between linear functions and linear inequalities of one variable?

From the relationship between the above two questions, we can get the relationship between "solving the inequality ax+b>0" and "finding the range of the independent variable x and the value of the linear function y=ax+b greater than 0". The essence is It’s the same problem as above.

Since any linear inequality of one variable can be transformed into the form of ax+b>0 or ax+b<0 (a and b are constants, a≠0), the solution to the linear inequality of one variable can be seen as: when the value of the linear function is greater than (or When it is less than) 0, find the corresponding value range of the independent variable.

Solve the inequality 5x+4<2x+10 by drawing the graph of the function

Method 1: The original inequality can be reduced to 3x-6<0, and the image of the straight line y=3x-6 is drawn. It can be seen that when x<2, the point on this straight line is below the x-axis. That is, at this time y=3x-6<0, so the solution set of the inequality is: x<2.

Method 2: Treat both sides of the original inequality as two linear functions. Draw the straight line y=5x+4 and the straight line y=2x+10. It can be seen that the abscissa of their intersection is 2. When x>2, for the same x, the point on the straight line y=5x+4 is below the corresponding point on the straight line y=2x+10. At this time, 5x+4<2x+10, so the solution of the inequality The set is: x<2.

4. Summary review

1. What is the relationship between linear functions and linear inequalities of one variable?

Since any linear inequality of one variable can be transformed into the form of ax+b>0 or ax+b<0 (a and b are constants, a≠0), the solution to the linear inequality of one variable can be seen as: when the value of the linear function is greater than (or When it is less than) 0, find the corresponding value range of the independent variable.

2. In this section we learned to use the graph of a linear function to solve linear inequalities of one variable. Although the method may not be simple, we re-understand inequalities from the perspective of functions, discover the connection between linear functions and linear inequalities of one variable, and be able to intuitively see how to use graphics to represent the solutions to inequalities, which is very important for our future study.

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For more information about the PPT courseware "Linear Functions: Viewing Equations (Groups) or Inequalities from the Perspective of Functions", please click the "Linear Functions ppt Viewing Equations (Groups) or Inequalities from the Perspective of Functions" ppt tag.

"Looking at equations (groups) or inequalities from the perspective of functions" linear function PPT courseware 2:

"Looking at equations (sets) or inequalities from the perspective of functions" linear function PPT courseware 2 (1) Solving the equation: 2x+20=0 (2) When what is the value of x, the value of the function y=2x+20 is 0? Question ( What is the relationship between 1) and (2)? From the function graph, the straight line y=2x+20 intersects the x-axis..

"Looking at equations (groups) or inequalities from the perspective of functions" PPT courseware for linear functions:

"Looking at equations (groups) or inequalities from the perspective of functions" PPT courseware on linear functions Observation What is the relationship between the following two questions? (1) Solve the equation 2x+20=0 (2) When the independent variable x is what value, the value of the function y =2x+20 is 0? Solution: (1) 2x+20=0 (2) ..

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Update Time: 2024-10-05

This template belongs to Mathematics courseware People's Education Press Eighth Grade Mathematics Volume 2 industry PPT template

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