"Variables and Functions" First-time Function PPT Courseware 2

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"Variables and Functions" First-time Function PPT Courseware 2

question:

(1) The selling price of each movie ticket in a theater is 10 yuan. Suppose x tickets are sold for a movie and the box office revenue is y yuan. How to express y using a formula containing x?

(2) A weight is suspended from the lower end of a spring. If the original length of the spring is 10cm, each 1kg weight will make the spring extend 0.5cm. Assume the mass of the weight is mkg, and the length of the spring after being stressed is lcm. Fill in the following table, And use the formula containing m to express l.

1. Definition of variables and constants

In a process of change, the quantity whose value changes is called a variable. The quantity whose value never changes is called a constant.

1. The school purchases a certain type of pen as a prize for students. The unit price of the pen is 4 yuan/piece. Then the relationship between the total amount y (yuan) and the number of purchased pieces x (pieces) is ________, where the variable is ________ , the constant is ________.

2. Plan to purchase 50 yuan of table tennis balls. The relationship between the total number n (pieces) that can be purchased and the unit price a (yuan) is _________, where the variable is ________ and the constant is _________.

2. Definition of function

Generally, 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, we say that x is the independent variable and y is the dependent variable. , at this time it is also said that y is a function of x.

If y=b when x=a, then b is called the value of the function when the value of the independent variable is a.

Knowledge feedback

1. There are 500 notebooks, and there are x students. If each student has 5 notebooks, then there will be y notebooks left. Using a formula containing ____quantity.

2. Xiao Zhang is going to save some of his usual pocket money and save it. He has saved 50 yuan and will save 12 yuan at the end of every month from now on. Assume that the number of Xiao Zhang’s deposits after The independent variable is ________, and ________ is a function of ________.

3. A car drives from a certain place to Shanghai, which is 500 kilometers away. Its average speed is 100 kilometers/hour.

(1) Write the functional relationship between the distance s (kilometers) of the car from Shanghai and the driving time t (hours).

(2) Point out the value range of the independent variable t.

(3) After driving for 3 hours, how many kilometers are there from Shanghai?

Solution: (1)s=500-100t.

(2)0≤t≤5.

(3) When t=3, s=500-100×3=200. After driving for 3 hours, the car is still 200 kilometers away from Shanghai.

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Update Time: 2024-10-03

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