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"Looking at equations (groups) or inequalities from the perspective of functions" PPT courseware for linear functions
observe
How are the following two questions related?
(1) Solve the equation 2x+20=0
(2) When the independent variable x has what value, the value of the function y =2x+20 is 0?
Solution: (1) 2x+20=0 (2) Let y=0, that is
2x=-20 2x+20=0
x=-10 2x=-20
x=-10
The two questions are actually the same question.
show the talent
1. The coordinates of the intersection of the straight line y=x+3 and the x-axis are ______, so the solution to the corresponding equation x+3=0 is ______.
2. Assume m and n are constants and m≠0, and the straight line y=mx+n (as shown in the figure), then the solution of the equation mx+n=0 is ______.
3. For y1=2x-1, y2=4x-2, the following statements are made:
①The two straight lines are parallel; ②The two straight lines intersect the y-axis at the same point; ③The two straight lines intersect the x-axis at the same point; ④The solutions of equations 2x-1 =0 and 4x-2=0 are the same; ⑤When x=1 , y1=y2=1. The correct one is ____ (fill in the serial number)
reward
Solving the linear equation ax+b=0 (a, b is a constant) can be transformed into: when the value of a linear function is 0, find the value of the corresponding independent variable. Graphically, this is equivalent to knowing the straight line y=ax+b and determining the value of the abscissa of its intersection with the x-axis.
Practice in class:
It is known that y1=-x+3, y2=3x-4, when x takes what value, how do you do y1>y2? Communicate with peers.
Do it:
The two brothers raced. The elder brother first asked his younger brother to run 9m, and then he started running. It is known that the younger brother runs 3 meters per second and the older brother runs 4 meters per second. List the functional relationship expressions, make a graph of the function, observe the graph and answer the following questions:
(1) When did the elder brother catch up with the younger brother?
(2) When does the younger brother run ahead of the older brother?
(3) When does the elder brother run ahead of the younger brother?
(4) Who ran 20m first? Who ran 100m first?
(5) How did you solve it? Communicate with peers.
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"Looking at equations (groups) or inequalities from the perspective of functions" linear function PPT courseware 3:
"Looking at equations (groups) or inequalities from the perspective of functions" PPT courseware for linear functions 3 1. Scenario introduction 1. Solve the inequality 5x+63x+10. Solution: The inequality 5x+63x+10 can be transformed into 2x-40. Solve this inequality to get x2. Thinking: Can all the inequalities be transformed...
"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..