"Logarithmic Function" Exponential function and logarithmic function PPT courseware (the concept, image and properties of logarithmic function in the first lesson)

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"Logarithmic Function" Exponential function and logarithmic function PPT courseware (the concept, image and properties of logarithmic function in the first lesson)

Part One: Learning Objectives

1. Understand the concept of logarithmic function and be able to find the domain of logarithmic function. (main difficulty)

2. Be able to draw the graph of a specific logarithmic function and explain the properties of the logarithmic function based on the graph of the logarithmic function. (emphasis)

core competencies

1. Cultivate intuitive imagination literacy by learning the graphics of logarithmic functions.

2. Cultivate the literacy of mathematical operations with the help of solving the domain of logarithmic functions.

Logarithmic function PPT, part 2: independent preview and exploration of new knowledge

1. The concept of logarithmic function

The function y=______(a>0, and a≠1) is called a logarithmic function, where is the independent variable, and the domain of the function is ______.

Thinking 1: Is the function y=2log3x, y=log3(2x) a logarithmic function?

Tip: No, it does not conform to the form of a logarithmic function.

2. Graph and properties of logarithmic function

Thinking 2: Who is related to the "rise" or "fall" of the logarithmic function?

Tip: The relationship between the base a and 1 determines the rise and fall of the logarithmic function.

When a>1, the graph of the logarithmic function "rises"; when 0

3. Inverse function

The exponential function ________(a>0, and a≠1) and the logarithmic function y=______________ are inverse functions of each other.

First try

1. The graph of the function y=logax is as shown in the figure, then the possible values ​​of the real number a are ()

A． 5B.15C.1eD.12

2. If the logarithmic function passes through the point (4,2), its analytical formula is ________.

3. The domain of function f(x)=log2(x+1) is ________.

Logarithmic function PPT, the third part: cooperative exploration to improve literacy

The concept and application of logarithmic function

[Example 1] (1) The function given below: ①y=log5x+1;

②y＝logax2(a>0, and a≠1); ③y＝log(3-1)x;

④y＝13log3x; ⑤y＝logx3(x>0, and x≠1);

⑥y=log2πx. Which is the logarithmic function is ()

A． ③④⑤　B． ②④⑥

C. ①③⑤⑥ D. ③⑥

(2) If the function y=log(2a-1)x+(a2-5a+4) is a logarithmic function, then a=________.

(3) It is known that the graph of the logarithmic function passes through the point (16,4), then f12=__________.

(1)D　(2)4　(3)－1　(1) It is known from the definition of logarithmic function that ③⑥ are logarithmic functions, so D is selected.

(2) Because the function y=log(2a-1)x+(a2-5a+4) is a logarithmic function,

So 2a-1>0, 2a-1≠1, a2-5a+4=0,

Solve to get a=4.

domain of logarithmic function

[Example 2] Find the domain of the following functions:

(1)f(x)=1log12x+1;

(2)f(x)=12-x+ln(x+1);

(3)f(x)=log(2x-1)(-4x+8).

regular method

Principles to be followed when finding the domain of a logarithmic function

1The denominator cannot be 0.

2When the radical exponent is an even number, the radicand is non-negative.

3The true number of logarithms is greater than 0, and the base is greater than 0 and not 1.

Reminder: The domain is the set of values ​​of the independent variables that make the analytical expression meaningful. When solving domain problems related to the logarithmic function, pay attention to the concept of the logarithmic function. If the independent variable is a true number, it must be true. The number is greater than 0; if the independent variable is on the base, it should be ensured that the base is greater than 0 and not equal to 1.

Graph problem of logarithmic function

[Inquiry Questions]

1. As shown in the figure, curves C1, C2, C3, and C4 correspond to the images of y=loga1x, y=loga2x, y=loga3x, and y=loga4x respectively. Can you point out the size relationship between a1, a2, a3, a4, and 1?

Tip: Draw a straight line y=1. The abscissa of the intersection point with each curve C1, C2, C3, C4 is the base of each logarithm. From this, it can be judged that the size of each base must be a4>a3>1>a2> a1>0.

2. What are the characteristics of the graphs of the functions y=ax and y=logax (a>0 and a≠1)?

Tip: The graphs of the two functions are symmetrical about the straight line y=x.

regular method

Transformation rules of function graphs

1Generally, the graph of the function y=fx±a+ba, b is a real number is the graph of the function y=fx translated left or right along the x-axis| a| units in length, and then translated up or down along the y-axis by |b| units in length.

2The image of a function containing absolute value is generally obtained by symmetric transformation. Generally, the image of y=f|x-a| is an axis-symmetric figure that is symmetrical about the straight line x=a ;The graph of function y＝|fx| is the same as the graph of y＝fx in the part where fx≥0, and about the part in fx<0 Symmetrical about the x-axis.

Class summary

1. The key to judging whether a function is a logarithmic function is to analyze whether the given function has the form y=logax (a>0 and a≠1).

2. In the logarithmic function y=logax, the base a directly affects its image. Learn to understand and master the image and properties of the logarithmic function from a classification perspective.

3. Issues involving the domain of logarithmic functions are often analyzed from the two perspectives of true numbers and base numbers.

Logarithmic function PPT, the fourth part: reaching the standard in class and solidifying the double base

1. The key to judging whether a function is a logarithmic function is to analyze whether the given function has the form y=logax (a>0 and a≠1).

2. In the logarithmic function y=logax, the base a directly affects its image. Learn to understand and master the image and properties of the logarithmic function from a classification perspective.

3. Issues involving the domain of logarithmic functions are often analyzed from the two perspectives of true numbers and base numbers.

2. Which of the following functions is a logarithmic function ()

A． y＝2＋log3x

B． y=loga(2a)(a>0, and a≠1)

C. y=logax2(a>0, and a≠1)

D. y＝lnx

3. The domain of function f(x)=lg x+lg(5-3x) is ()

A.0,53

B.0,53

C.1,53

D.1,53

4. It is known that f(x)=log3x.

(1) Make a graph of this function;

(2) If f(a)

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For more information about the PPT courseware "Exponential Functions and Logarithmic Functions, Logarithmic Functions, Logarithmic Functions, Conceptual Images and Properties of Logarithmic Functions", please click on the Exponential Functions and Logarithmic Functions ppt Logarithmic Functions ppt Conceptual Images and Properties of Logarithmic Functions ppt tag .

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Update Time: 2024-09-11

This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template

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