"Variables and Functions" One-time Function PPT Courseware 6

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"Variables and Functions" One-time Function PPT Courseware 6

question:

(1) The selling price of each movie ticket is 10 yuan. If 150 tickets are sold in the morning show, 205 tickets are sold in the matinee, and 310 tickets are sold in the evening show, how much are the box office revenue of each of the three movies? Assume that a movie receives x tickets and the box office revenue is y yuan. How to express y using a formula containing x? Y= 10x

(2) Hang a medium weight on the lower end of a spring, change and record the mass of the weight, and observe and record the changing pattern of the spring length. If the original length of the spring is 10cm, and every 1kg weight makes the spring extend 0.5cm, how to use it? The formula containing the weight m (unit: kg) represents the length of the spring l (unit: cm) after force is applied?

L=10+0.5m

(3) To draw a circle with an area of ​​10cm2, what should be the radius of the circle? The area of ​​the circle is 20cm2? How to express the radius r of a circle using a formula containing the area S of a circle?

In a certain change process, quantities that can take on different values ​​are called variables.

In the process of studying the problem, there is another quantity whose value always remains unchanged, which we call a constant.

Example 1 Write down the relational expressions satisfied in each of the following problems, and point out which quantities are variables and which quantities are constants in each relational expression?

A rectangular site is surrounded by a fence with a total length of 60m. Find the relationship between the area S (m2) of the rectangle and the length of one side x (m);

When purchasing pencils with a unit price of 0.4 yuan, the relationship between the total amount y (yuan) and the number of pencils purchased n (pieces);

An athlete trains on a 4000m lap track. The relationship between the time t (s) it takes for him to run a lap and the running speed v (m/s);

The bank stipulates that the annual interest rate of a five-year deposit is 2.79%. Then the relationship between the principal of a person's deposit of x yuan and the principal and interest earned is y (yuan).

Exercise: 1. Point out the constants and variables in the following equations respectively.

(1) The formula for the area of ​​a circle is S=πr2;

(2) l=4a for square;

(3) The unit price of rice is 2.50 yuan/kg, then the relationship between the quantity x (kg) of rice purchased, the amount, and the amount y is y=2.5x.

2. Write the relational expressions of the following questions and point out the constants and variables.

(1) The monthly interest rate of a certain current savings is 0.16%. If you deposit a principal of 10,000 yuan, according to national regulations, when you withdraw money, you should pay 20% interest tax on the interest. Find the real income of this current savings after deducting the interest tax. The relationship between the principal and interest and y (yuan) and the number of months saved x.

(2) As shown in the figure, each figure is a pattern composed of several potted flowers. Each edge (including two vertices) has n potted flowers. The total number of pots in each pattern is S. Find the relationship between S and n. Mode.

induction:

Ask students to think about the rules for the value range of function independent variables.

(1) There is a denominator, and the denominator cannot be zero.

(2) When opening an even number to the power, the radicand is a non-negative number.

(3) Zero power, the base cannot be zero

(4) It is a practical problem, and practical problems must be meaningful

Let’s practice in practice!

Write the relationship expressions in each of the following questions and point out the constants and variables

(1) The relationship between the circumference C and the radius r of a circle;

(2) When a train travels at a speed of 60 kilometers/hour, the relationship between the distance s (kilometers) it travels and the time t (hours) it takes;

(3) The relationship between the sum of the interior angles S of an n-sided polygon and the number of sides n.

Classroom test:

1. In y=3x+1, if x is an independent variable, ________ is a function of x

2. Among the following statements, which one is incorrect ( )

A. A function is not a number, but a relationship

B. The sum of the interior angles of a polygon is a function of the number of sides

C. Time of day is a function of temperature

D. Temperature is a function of time throughout the day

3. The side length of the square is 5 cm. When the side length is reduced by x cm, the perimeter is y cm. Find the functional relationship between y and x.

Extended migration: A car has 30 liters of oil in its fuel tank, and consumes 2.5 liters of fuel per 100 kilometers while driving. Assume that the mileage traveled is functional relationship between?

When x=10, y=?

When x=12, y=?

When x=12.1, y=?

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For more information about the PPT courseware "Primary Function Variables and Functions", please click the "Primary Function ppt Variables and Functions ppt" tab.

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Update Time: 2024-07-08

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