"Logarithmic Function" Exponential function and logarithmic function PPT (differences in the growth of different functions in Lesson 3)

"Logarithmic Function" Exponential function and logarithmic function PPT (differences in the growth of different functions in Lesson 3)

Part One: Learning Objectives

Understand commonly used function models that describe different growth laws in the real world, and understand the meaning of growth such as linear rise, exponential explosion, logarithmic growth, etc.

Ability to select function models based on specific problems and construct function models to solve problems

Logarithmic function PPT, part 2: independent learning

Problem guide

Preview the textbook P136-P138 and think about the following questions:

1. What is the monotonicity of the functions y=kx(k>0), y=ax(a>1) and y=logax(a>1) on (0, +∞)?

2. What are the differences in the growth rates of the functions y=kx(k>0), y=ax(a>1) and y=logax(a>1)?

A preliminary exploration of new knowledge

Properties of the three functional models

self-test

Judge whether it is true or false (mark “√” if it is correct and “×” if it is wrong)

(1) The function model with constant growth rate is a linear function model. ()

(2) The function y=x2 grows faster than y=2x. ()

(3) When a>1, k>0, for ∀x∈(0, +∞), there is always logax

Among the following functions, the one that increases as x increases and is the fastest is ()

A． y＝ex B． y=lnx

C. y=2x D． y=e-x

It is known that y1=2x, y2=2x, y3=log2x, when 2

A． y1>y2>y3 B． y2>y1>y3

C. y1>y3>y2 D． y2>y3>y1

Logarithmic function PPT, the third part: lecture and practice interaction

Growth differences in functional models

The data of the four variables y1, y2, y3, y4 changing with the variable x is as shown in the table:

The variable that changes exponentially with respect to x is ________.

[Analysis] Observe the increased value of function values ​​y1, y2, y3, y4 from the table. Which variable has the largest increased value, then the variable changes exponentially with respect to x.

Variables that grow explosively change exponentially.

It can be seen from the table that the four variables y1, y2, y3, and y4 all change from 2. The variables y1, y2, y3, and y4 are getting larger and larger, but the growth rates are different. Among them, the growth rate of variable y2 The fastest, draw their images (figure omitted), it can be seen that the variable y2 changes as an exponential function with respect to x. Therefore fill in y2.

regular method

Common function models and growth characteristics

(1) Linear function model: The growth characteristic of the linear function model y=kx+b(k>0) is a straight rise, and its growth rate remains unchanged.

(2) Exponential function model: The growth characteristic of the exponential function model y=ax(a>1) is that as the independent variable increases, the function value increases faster and faster, that is, the growth rate is sharp, which is vividly called "Exponential explosion".

(3) Logarithmic function model: The growth characteristic of the logarithmic function model y=logax(a>1) is that as the independent variable increases, the function value increases slower and slower, that is, the growth rate is gentle.

Four objects move forward from a certain point at the same time. The functional relationship of their distance fi(x)(i=1, 2, 3, 4) with respect to time x(x>1) is f1(x)=x2, f2( x)=2x, f3(x)=log2x, f4(x)=2x, if they keep moving, the final functional relationship of the object at the front is ()

A． f1(x)=x2 B. f2(x)＝2x

C. f3(x)=log2x D． f4(x)＝2x

Selection of function model

An automobile manufacturer announced in early 2019 that the company planned to set its production target for 2019 at 430,000 vehicles. It is known that the company's automobile production volume in the past three years is shown in the following table:

Year 2016 2017 2018

Output 8(thousand) 18(thousand) 30(thousand)

If we define 2016, 2017, 2018, and 2019 as the first, second, third, and fourth years respectively. There are now two function models: quadratic function model f(x)＝ax2＋bx＋c(a≠0), exponential function model g(x)＝a·bx＋c(a≠0, b＞0, b≠1), which model Can it better reflect the relationship between the company's production volume y and year x?

regular method

Selection criteria for different function models

Different function models can describe different change patterns in the real world:

(1) The linear function growth model is suitable for describing the change pattern of constant growth rate;

(2) The exponential function growth model is suitable for describing the rapid changes in growth rate;

(3) The logarithmic function growth model is suitable for describing the change pattern of gentle growth rate;

(4) The power function growth model is suitable for describing the general change law of growth rate.

Logarithmic function PPT, part 4: feedback on compliance with standards

1. Among the following functions, the one whose growth rate is getting slower and slower is ()

A． y=6x B. y＝log6x

C. y=x6 D． y=6x

Analysis: Choose B. The growth rate of the linear function in D remains unchanged, the growth rate of the functions in A and C is getting faster and faster, and only the growth rate of the logarithmic function in B is getting slower and slower, which is in line with the meaning of the question.

2. For example, the table is a set of data in which the function value y changes with the independent variable x. From this, it can be judged that its most likely function model is ()

A. Linear function model B. quadratic function model

C. Exponential function model D. Logarithmic function model

Analysis: Choose A. As the independent variable increases by 1, the function value increases by 2. The increment of the function value is uniform, so it is a linear function, that is, a linear function model.

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For more information about the PPT courseware "The Difference in the Growth of Different Functions between Exponential and Logarithmic Functions and Logarithmic Functions", please click the Difference in Growth of Different Functions ppt between Exponential Functions and Logarithmic Functions ppt Logarithmic Function ppt tag.

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