"Variables and Functions" First Time Function PPT Courseware 4

Description

"Variables and Functions" First Time Function PPT Courseware 4

Situation introduction

(1) Have you ever ridden a Ferris wheel? When you sit on the Ferris wheel, how does your height h from the ground change as time t changes?

variable

The quantities that describe the rotation process of the Ferris wheel are time t and height h. The height h changes with the change of time t, and they will take different values.

Quantities that can take on different values ​​during a certain change process are called variables.

As the deposit period x grows, the corresponding annual interest rate y also grows.

In the above change process, there are two variables: deposit period x and annual interest rate y.

For each value of the deposit period x, the annual interest rate y has a unique value corresponding to it.

Let us say that the deposit period x is the independent variable and the annual interest rate y is the dependent variable.

It is also said that the annual interest rate y is a function of the deposit period x.

generalize

Variable: A quantity that can take on different values ​​during a certain change process is called a variable.

Constant: In the process of researching a problem, there is another quantity whose value always remains unchanged, which we call a constant. Such as 300 000 in question three and π in question four.

The concept of function

In each of the above questions, two variables appear, and they are interdependent and closely related.

Generally, if there are two variables in a change process, such as x and y, and for each value of x, y has a unique value corresponding to it, 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.

think

1. Among the various functions that appear in the above "Try it", are there any restrictions on the values ​​of the independent variables? If so, write down its value range.

y=10-x (x is a natural number from 1 to 9)

y=180°-2x(0＜x＜90°)

y=1/2x²(0≤x≤10)

2. In question 1 above, when the horizontal addend of the black grid is 3, what is the vertical addend? When the vertical addend is 6, what is the horizontal addend?

For the function in question 1, when the independent variable x=3, the corresponding function y

The value of y=10-3=7, then use 7 as the function value when x=3

Example 1 Find the value range of the independent variable x in the following function:

(1) y＝3x-1; (2) y＝2x2+7;

(3) y=1/x+2; (4) y=√x-2.

Solution: x in (1) (2) takes any real number, 3x-1, 2x²+7 are all meaningful

In (3), when x≠-2, the original formula is meaningful.

(4) When x≥2, the original formula is meaningful.

Talk about it

What I learned from this class is...

1. Use one variable to represent another variable.

2. The concepts of variables, constants and functions.

3. The value range and function value of the independent variable.

Keywords: First-time function teaching courseware, Variables and functions teaching courseware, New People's Education Edition eighth-grade mathematics second volume PPT courseware, Eighth-grade mathematics slide courseware download, First-time function PPT courseware download, Variables and functions PPT courseware download, .ppt format

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

"Variables and Functions" One-time Function PPT Courseware 7:

"Variables and Functions" linear function PPT courseware 7 Question 1: The car is traveling at a constant speed of 60 kilometers per hour, the mileage is s kilometers, and the driving time is t hours. First fill in the table below, and then try the formula containing t Sub represents s. Question 2: The selling price of each movie ticket is...

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

"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 were the box office receipts of each of the three movies? Suppose a movie requires x tickets..

"Variables and Functions" First-time Function PPT Courseware 5:

"Variables and Functions" One-time Function PPT Courseware 5 Banks have stipulated corresponding interest rates for various deposit methods. The following table is the annual interest rate stipulated by the People's Bank of China for lump sum deposits and withdrawals in August 2006: Observation 1 Table, talk about the growth of the deposit period x, relative...

File Info

Update Time: 2024-06-27

This template belongs to Mathematics courseware People's Education Press Eighth Grade Mathematics Volume 2 industry PPT template

Preview