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"Function" One-time function PPT courseware 5
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Thinking: 1. How many variables are there in each problem?
2. What are the connections between variables in the same problem?
Question 1: The National Games torchbearer runs at a speed of 3 meters/second to pass the torch. The passing distance is S meters and the passing time is t seconds. Fill in the following table:
How to express s using the formula containing t? S=3t
The transmission distance S changes with the change of transmission time t,
When the delivery time t determines a value, the delivery distance S determines a value accordingly.
Question 2
The length of the spring is related to the weight attached. If the original length of the spring is 10cm, and every 1 kilogram of weight causes the spring to extend by 0.5cm, try filling in the table below.
How to express the spring length L (cm) after being stressed using a formula containing the weight mass m (kg)?
L=10+0.5m
comparative thinking
What do the above three questions have in common?
1. There are two variables in every change process.
2. When one variable determines a value, another variable has a uniquely determined value corresponding to it.
The concept of function:
1. 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 the independent variable and y is the independent variable of x. function.
2. If y=b when x=a, then b is called the function value when the value of the independent variable is a.
Walking in groups to help each other
1. There is currently 40L of gasoline in the fuel tank of a car. If there is no more refueling, the amount of fuel y (unit: L) in the fuel tank will decrease with the increase of the mileage x (unit: km). The average fuel consumption is 0.1 L/km.
(1) Write an expression expressing the functional relationship between y and x.
(2) Point out the value range of the independent variable x.
(3) How much fuel is left in the fuel tank when the car travels 300 km?
Solution: (1) The functional relationship is: y = 40-0.1x
(2) From x≥0 and 40-0.1x ≥0, we get 0 ≤ x ≤ 400
∴The value range of the independent variable is: 0 ≤ x ≤ 400
(3) When x = 300, the value of function y is: y=40-0.1×300=10
Therefore, when the car travels 300 km, there is still 10L of oil in the fuel tank.
2. The perimeter of the isosceles triangle ABC is 10, the length of the base BC is y, and the length of the waist AB is x. Find:
(1) An expression expressing the functional relationship between y and x.
(2) The value range of the independent variable;
(3) When the waist length AB=3, find the length of the base.
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