"Function" One-time function PPT courseware 2

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"Function" One-time function PPT courseware 2

Review old knowledge

1. As shown in the figure, the height of the cone is 4 cm. When the base radius r of the cone changes from small to large, the volume V of the cone also changes accordingly.

(1) How to express the relationship between V and r using mathematical formulas?

(2) What quantities are V and r respectively?

Both V and r are variables, r is called the independent variable, and V is called the dependent variable.

(3)What are the constants?

Cylindrical objects such as bottles or cans are often stacked as shown below. As the number of layers increases, how does the total number of objects change?

For a given number of layers n, the corresponding total number of objects y is uniquely determined.

On a flat road, a certain model of car will still slide s meters after emergency braking. Generally, there is an empirical formula S=v²/300, where v represents the speed of the car before braking (unit: kilometers/hour).

(1) Calculate what is the corresponding sliding distance s when v is 50, 60, and 100 respectively?

(2) Given a value of v, can you find the unique corresponding value of s?

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?

y is a function of m

(1) How does it represent functions?

(2) What are the characteristics of functions represented by list method?

(3) It is known that the length of diagonal AC of rhombus ABCD is 4, and the length x of BD is changing, then the area of ​​the rhombus is:

Class summary

1. The concept 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 and y is the dependent variable.

2. Representation method of function:

(1) Image method: image and intuition;

(2) List method: specific and accurate;

(3) Analytical method: abstract and comprehensive.

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Update Time: 2024-10-02

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