"Function and Its Representation" PPT Courseware 3

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"Function and Its Representation" PPT Courseware 3

Observe and think

Do you remember what a function is?

In real life, functional relationships exist everywhere.

Do you know what are the common ways to express functional relationships?

function definition

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

How to express functional relationships

The mathematical expressions used to express functional relationships are called functional analytical expressions or functional relational expressions.

(1) The method of expressing functions using mathematical formulas is called analytical method

(2) The method of using tables to express functional relationships is called the list method

(3) The method of using images to represent functional relationships is called the image method

1. When a car is driving, the speed v changes with time t as shown in the figure.

(1) In this problem, how is the functional relationship between speed y and time t expressed?

image method

(2) What is the value range of time t?

0≤t≤7

2. As shown in the figure, the equilateral triangle ABC is inscribed in the circle O. Let the radius of the circle be r. Try to write down the functional relationship between the area S and r of the shaded part in the figure. Which method is used to express the functional relationship between them?

S=πr²-3/4√3r²

Exercise 1:

Find the range of values ​​that the independent variable x can take in the following functions:

(1) y=3x-1/2 (2) y=1/2x+1

(3) y=√6-2x (4) y=1/√3x+1

Exercise 2:

The perimeter of isosceles triangle ABC is 10cm, the length of base BC is y (cm), and the length of waist AB is x (cm)

(1) Write the analytical expression of the function between y and x;

y=10-2x

(2) Point out the range of values ​​that the independent variable x can take.

2.5＜x＜5

Exercise 3:

There is 300L of oil in the fuel tank. The oil flows out of the pipe at a constant speed and finishes in 1 hour.

Write the analytical formula of the function between the amount of oil Q (L) remaining in the tank and the oil outflow time t (s), and point out the range of values ​​that the independent variable t can take.

Function analytical formula: Q=300-1/12t

The value range of t: 0≤t≤3600

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"Function and Its Representation" PPT Courseware 2:

"Function and Its Representation" PPT Courseware 2 Learning Objectives 1. Understand the concept of function, and be able to judge whether the relationship between two variables satisfies a functional relationship; 2. Understand the representation methods of functions, and be able to flexibly use these representation methods to express A function; 3. Understand functions..

"Function and Its Representation" PPT courseware:

"Function and Its Representation" PPT courseware teaching target knowledge and skills: 1. Enable students to use lists, points, and connected lines to draw function images. 2. Learn to observe and analyze function image information, and interpret images, that is, Can understand abstract quantitative relationships from images. Process and...

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Update Time: 2024-08-11

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

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