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"Function" One-time function PPT courseware 3
think about it
Have you ever ridden a Ferris wheel? When you sit on a Ferris wheel, how does your height above the ground change over time? Please talk about your feelings.
For a given time t , is the corresponding height h determined?
Among them, for each given time t, how many values does the height h have?
In the first grade of junior high school, we studied "The Relationship between Variables". How many variables are there in the above problem? What method is used to express their changing relationship?
What do the three questions above have in common?
There are two variables: ① time t, corresponding height h; ② number of layers n, total number of objects y; ③ car speed v, sliding distance s. If the value of one of the variables (the independent variable) is given, the value of the other variable (the dependent variable) is determined accordingly.
Generally, in a certain change process, there are two variables x and y. If an x value is given, a y value is determined accordingly, then we call y a function of x, where x is the independent variable. , y is the dependent variable.
practice
How many variables are there in each of the following questions? Can you think of one of the variables as a function of the other?
(1) Each student buys an algebra book. The unit price of the book is 2 yuan, so x students pay a total of y yuan. y = 2x
(2) If you plan to buy 50 yuan of table tennis balls, the relationship between the total number of purchases y (pieces) and the unit price x (yuan). y =50/x
(3) The volume of a copper ball at 0°C is 1000cm3. For every 1°C increase in temperature after heating, the volume increases by 0.051cm3. The volume of the ball at t°C is Vcm3. V=0.0051t+1000
What did you gain from this lesson?
1. Definition of function:
Generally, in a certain change process, there are two variables x and y. If an x value is given, a y value is determined accordingly, then we call y a function of x, where x is the independent variable. , y is the dependent variable.
2. Function representation:
Three methods can be used
①Image method,
②List method,
③Analytical expression method (relational expression method)
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