"Function and Its Representation" PPT Courseware 2

Description

"Function and Its Representation" PPT Courseware 2

learning target

1. Understand the concept of function and be able to judge whether the relationship between two variables satisfies the functional relationship;

2. Understand the representation methods of functions, and be able to flexibly use these representation methods to represent a function;

3. Understand the essential meaning of functions and be able to find the value range of function independent variables.

Observe and think:

Example 1: A hydrological station on a tributary of the Yellow River recorded the changes in the river water level in the tributary from 9:00 to 21:00 that day. What information can you obtain from it?

Example 2. The original length of a spring is 15cm. The tensile force at one end of the spring does not exceed the elastic limit of 40N. For every 10N of additional tensile force, the spring stretches 2cm. Please fill in the following table:

Example 3: An object falls freely from a height of 490m. The relationship between the height h (m) of the object from the ground and the time t (s) of the object falling satisfies the expression:

Observe and think:

1. Among these questions, are they related to the changing relationship between several variables? What are the independent variables? What are their value ranges?

2. In these questions, for every certain value that the independent variable takes within the range of possible values, is the value of the other variable uniquely determined?

Inductive conclusion

In these problems, for every definite value of the independent variable, there is a unique corresponding value of the other variable.

This relationship can be summarized in four words: one-to-one correspondence

1. (1) The concept of function

This one-to-one correspondence also has another name: function

The concept of function:

In the same change process, there are two variables x and y. If for every definite value that variable x takes within the range of possible values, variable y has a unique and definite value corresponding to it, then y is said to be a function of x.

(2) Representation method of function

Function is a one-to-one correspondence, so in what ways can this relationship be expressed?

1.Image method

2. List method

3. Analytical method

This section requires:

1. Understand the definition of functions and be able to judge whether the relationship between two variables is a functional relationship;

2. Be able to use three representation methods to represent functional relationships, and be able to obtain the changing rules between variables from these representation methods.

Small scale chopper:

1. Are the corresponding relationships between the variable y and the variable x represented in the following four figures all functional relationships?

2. Assume x is a non-negative number. If y is the arithmetic square root of x, when x changes, is y a function of x? What if y is the negative square root of x? What if y is the square root of x? If so, please write the function expressions between them respectively.

Inductive improvement:

For a function expression expressed analytically, in order to determine the range of values ​​that its independent variables can take, the function expression must be meaningful. When solving real problems, you also need to make real problems meaningful.

Summary of this section

1. Understand the concept of functions: one-to-one correspondence

2. Representation methods of functions: image method, list method, analytical method

3. Find the value range of the independent variables in the functional relationship represented by the analytical method: pay attention to considering the meaning and practical significance of the analytical expression

Challenge yourself: If the range of values ​​for the independent variable x in the function y=1/x²-2x+m is all real numbers, can you determine the value range of m?

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For more information about the "Function and Its Notation" PPT courseware, please click the "Function and Its Notation" ppt tab.

"Function and Its Representation" PPT courseware 3:

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"Function and Its Representation" PPT courseware:

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Update Time: 2024-09-04

This template belongs to Mathematics courseware Qingdao Edition Ninth Grade Mathematics Volume 2 industry PPT template

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