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"Variables and Functions" One-time Function PPT Courseware
During a change process, we call the quantity whose value changes as a variable. The value of some quantities never changes, and we call them constants.
(1) Constants and variables:
In a change process: the changed quantity is called ________; the unchanged quantity is called ________
(2) Point out the constants and variables in the previous three questions.
(1) In the "trip problem", s=60t, the constant is ________, and the variable is ________
(2) "Spring elongation problem", L=10+0.5m, the variable is ________; the constant is ________
(3) In "Box Office Revenue Problem", y=10x, the constant is ________, and the variable is ________;
The concept of function:
In a change process, if there are two variables x and y, and for every certain value of x, y has a unique corresponding value, then we say that x is an independent variable and y is a function of x.
For example: in y=60x, when x=2, y=120, then 120 is called the function value when the value of the independent variable is 2.
Explore:
A water tank filled with 10 kilograms of water flows out of 0.5 kilograms of water per hour. How to express the functional relationship between the remaining water volume y (kilograms) in the water tank and time t (hours)?
y=10-0.5t
Please write the value range of the independent variable t.
From t≥0 and 10-0.5t ≥0, we get 0 ≤ t≤ 20
∴The value range of the independent variable is: 0 ≤ t ≤ 20
When the time is 6 hours, find the amount of water remaining in the water tank
When t = 6, the value of function y is: y=10-0.5×6=7
Note: For practical problems, the value range of the independent variables should also make the actual problem meaningful.
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